Useful for all Agricultural, Medical, Pharmacy and Engineering Entrance Examinations
India.
held across
STD. XI Sci.
Triumph Physics
Based on Maharashtra Board Syllabus
Salient Features
• Exhaustive subtopic wise coverage of MCQs
• Important formulae provided in each chapter
• Hints included for relevant questions
• Various competitive exam questions updated till the latest year
• Includes solved MCQs from JEE (Main), AIPMT, NEET P-I, K CET 2015 and
2016
• Includes solved MCQs uptill MH CET 2014
• Evaluation test provided at the end of each chapter
Solutions/hints to Evaluation Test available in downloadable PDF format at
www.targetpublications.org/tp10142
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P.O. No. 28098
10142_10921_JUP
Preface
“Std. XI: Sci. Triumph Physics” is a complete and thorough guide to prepare students for a competitive
level examination. The book will not only assist students with MCQs of Std. XI but will also help them to prepare
for JEE, AIPMT, CET and various other competitive examinations.
The content of this book is based on the Maharashtra State Board Syllabus. Formulae that form a vital
part of MCQ solving are provided in each chapter. Notes provide important information about the topic.
Shortcuts provide easy and less tedious solving methods. Mindbenders have been introduced to bridge the gap
between a text book topic and the student’s understanding of the same. A quick reference to the notes, shortcuts
and mindbenders has been provided wherever possible.
MCQs in each chapter are divided into three sections:
Classical Thinking: consists of straight forward questions including knowledge based questions.
Critical Thinking: consists of questions that require some understanding of the concept.
Competitive Thinking: consists of questions from various competitive examinations like JEE, AIPMT,
MH CET, K CET, CPMT, GUJ CET, AP EAMCET (Engineering, Medical), TS EAMCET (Engineering,
Medical), Assam CEE, BCECE etc.
Hints have been provided to the MCQs which are broken down to the simplest form possible.
An Evaluation Test has been provided at the end of each chapter to assess the level of preparation of the
student on a competitive level.
An additional feature of pictorial representation of a topic is added to give the student a glimpse of
various interesting physics concept.
The journey to create a complete book is strewn with triumphs, failures and near misses. If you think
we’ve nearly missed something or want to applaud us for our triumphs, we’d love to hear from you.
Please write to us on : [email protected]
Best of luck to all the aspirants!
Yours faithfully
Authors
Sr. No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topic Name
Measurements
Scalars and Vectors
Projectile Motion
Force
Friction in Solids and Liquids
Sound Waves
Thermal Expansion
Refraction of Light
Ray Optics
Electrostatics
Current Electricity
Magnetic Effect of Electric Current
Magnetism
Electromagnetic Waves
Page No.
1
31
62
106
152
193
216
255
298
331
378
417
447
468
Chapter 01: Measurements
01
Measurements
Subtopics
Measuring the radius of the Earth
1.0
Introduction
1.1
Need for measurements
1.2
Units of measurements
1.3
System of units
1.4
S.I Units
1.5
Fundamental and derived units
1.6
Dimensional analysis
1.7
Order
of
magnitude
and
significant figures
1.8
Accuracy
and
measurements
errors
in
Eratosthenes was first to measure the radius of the
Earth using the difference in angle of shadows cast
at the same time in two different cities Syene (now
Aswan) and Alexandria. Using simple geometry, he
determined the degrees of arc between them to be 7°.
1
Std. XI : Triumph Physics
Formulae
1.
Notes
Measure of physical quantity (M):
Numerical value  size of unit. i.e., M = nu
For definite amount of physical quantity:
1
n
u
1
i.e., magnitude of physical quantity 
units
Conversion factor of a unit in two system of
units:
2.
3.
a
b
1.
Fundamental Quantity
Length
Mass
Time
Temperature
Electric current
Luminous intensity
Amount of substance
c
L  M  T 
n=  1  1  1
 L 2   M 2   T2 
Average value or mean value:
a + a 2 + a 3 + .... + a n
1 n
=  ai
am = 1
n i 1
n
4.
5.
If x = x1  x2, then maximum error in x:
x = x1 + x2
6.
If x = x1m  xn2 , then error in measurement:
x
mx1
nΔx 2
=
+
x
x1
x2
7.
Absolute error:
Average value  Measured value
| an | = | am  an |
Mean absolute error:
Δa1 + Δa 2 + ... + Δa n
1
=
| am | =
n
n
8.
9.
am
Derived units: These units depend upon
the fundamental units to give units of a
physical quantity.
i 1
2.
 100 %
The parallax method is used
i.
to measure separation between two
sources (i.e., two planets), if distance (b)
between them is very large.
O

Some practical units in term of S.I. unit
Practical units
1 Angstrom
1 Micron
1 Nanometer
1 Light year
1 Astronomical unit
1 Atomic mass unit
1 Torr
2
Abbreviation
Å
m/
nm
ly
AU
a.m.u./u
T
S.I. Unit
radian (rad)
steradian (sr)
Distance
Time
Thus its unit is m/s. It means that unit of
speed depends upon the fundamental
unit of length and time.
n
Percentage error:
a m
ii.
 a i
am
Relative error  100 =
Supplementary Quantity
Plane angle
Solid angle
S.I Unit
metre (m)
kilogram (kg)
second (s)
kelvin (K)
ampere (A)
candela (cd)
mole (mol)
For example: speed =
Relative (fractional) error:
a m
10.
Units are classified mainly into two groups.
i.
Fundamental units: These
are
independent of other units. The seven
fundamental quantities and their units
are given below.
S.I. unit
1010 m
106 m
109 m
9.46  1015 m
1.496  1011 m
1.66  1027 kg
1 mm of Hg
s
L
s=
s
b
R
Basis
b
=
θ
Parallactic angle
Chapter 01: Measurements
ii.
to find the size of an astronomical object.
A
D
iv.
B
 s
Mindbenders
O
EARTH
Linear diameter = distance
 angular diameter
D =s
3.
4.

If the error in measurement of ‘a’ is a
and the error in measurement of ‘b’ is
a
b then the percentage error in,
is
b
 a b 
 
  100
b 
 a
To determine dimensions of a physical
quantity, the unit of fundamental quantities
are represented by ‘L’ for length, ‘M’ for
mass, ‘T’ for time, ‘K’ for temperature, ‘I’ or
‘A’ for current, ‘C’ for luminous intensity and
‘mol’ for amount of substance.
1.
The dimensions of a physical quantity are
independent of the system of units.
2.
A physical quantity that does not have any
unit is always dimensionless.
3.
Angle is a special physical quantity which is a
ratio of two similar physical quantities i.e.,
arc/radius and requires a unit.
4.
In the formula,
[Mx Ly Tz]; if x = y = z = 0, then the quantity is
a dimensionless quantity.
Percentage error in different cases:
i.
If the error in ‘a’ is a, then the
a
percentage error in a =
 100
a
ii.
If the error in ‘a’ is a, then the
 a 
percentage error in an =  n 

 a 
100
iii. If the error in measurement of a is a
and the error in measurement of ‘b’ is
b then, the percentage error in ‘ab’ is
 a b 
 
  100
b 
 a
Examples of dimensionless quantities: Strain,
specific gravity, relative density, angle, solid
angle, poisson’s ratio, relative permittivity,
Reynold’s number, all the trigonometric
ratios, refractive index, dielectric constant,
magnetic susceptibility etc.
A dimensionless quantity has the same numeric
value in all the system of units.
Dimensions, units, formulae of some quantities:
Quantity
Speed
Formula
Distance
Time
Unit
Dimension
m s1
[M0L1T1]
Acceleration
Changein velocity
Time
m s2
[M0L1T2]
Force
Mass  Acceleration
N (newton)
[M1L1T2]
Pressure
Force
Area
N m2
[M1L1T2]
Mass
Volume
Force  distance
kg m3
[M1L3T0]
joule
[M1L1T2] [L1]= [M1L2T2]
Density
Work
3
Std. XI : Triumph Physics
Energy
joule
[M1L1T2] [L1]= [M1L2T2]
watt
[M1L2T3]
kg m s1
Ns
[M1L1T1]
[M1L1T1]
  rF
Nm
[M1L1T2] [L]= [M1L2T2]
-Energy
kelvin
joule
[M0L0T01]
[M1L2T2]
joule/kg K
[M0L2T–2–1]
joule/K
[M1L2T–2–1]
Force  distance
Momentum
Work
Time
Mass  Velocity
Impulse
Force  Time
Power
Torque
Temperature (T)
Heat (Q)
Specific heat (c)
Thermal capacity



Q
m
--
Latent heat (L)
heat ()
mass (m)
joule/kg
[M0L2T–2]
Gas constant (R)
PV
T
joule/mol K
[M1L2T–2–1]
joule/K
[M1L2T–2–1]
joule/m s K
[M1L1T–3–1]
watt/m2 K4
[M1L0T–3 –4]
mK
[M0L1T01]
Energy (E)
Frequency (F)
joule s
[M1L2T–1]
--
kelvin–1
[M0L0T0–1]
--
joule/calorie
[M0L0T0]
Current  Time
coulomb
[M0L0T1A1]
coulomb metre2
[M0L–2T1A1]
ampere
ampere/m2
[M0L0T0A1]
[M0L–2T0A1]
R
, N = Avogadro
N
number
From
Q
 T 
Coefficient of thermal t  KA  x 


conductivity (K)
Q  x  1
K


t  T  A
Boltzmann constant
(k)
Stefan's constant ()
Wien's constant (b)
Planck's constant (h)
Coefficient of linear
Expansion ()
Mechanical
equivalent of Heat(J)
Electric charge (q)
Surface charge
density()
Electric current (I)
Current density (J)
4
E
T4
b = Nm  T
=
=
charge
area
-Current per unit area
Electric potential (V)
Work
Charge
joule/ coulomb
[M1L2T–3A–1]
Intensity of electric
field (E)
Force
Charge
volt/metre, newton/coulomb
[M1L1T–3A–1]
Chapter 01: Measurements
Resistance (R)
P.D.
Current
volt/ampere or ohm
[M1L2T–3 A–2]
Conductance
1
R
ohm1
[M–1L–2T3A2]
Resistivity or
Specific resistance
()
Ra
l
ohm metre
[M1L3T–3 A–2]
Conductivity ()
1

ohm1metre1
[M–1L–3T3A2]
Electric dipole
moment (p)
q(2a)
coulomb metre
[M0L1T1A1]
coulomb 2
newton metre 2
[M–1L–3T4A2]
Unitless
[M0L0T0]
coulomb/ volt or farad
[M–1L–2T4A2]
volt  second
or henry or
ampere
ohm-second
[M1L2T–2 A–2]
henry
[M1L2T2A2]
wdt
q
volt-second or weber
[M1L2T–2 A–1]
B=
F
qv
newton
or
ampere metre
joule
or
ampere metre 2
volt second
or
metre 2
tesla
[M1L0T–2 A–1]
Magnetic intensity (H) H =
Idl
r2
ampere/ metre
[M0L–1T0 A1]
ampere metre2
[M0L2T0A1]
joule
newton
or
2
ampere
ampere 2 metre
volt second
or
or
ampere metre
ohmsecond
henry
or
metre
metre
[M1L1T–2 A–2]
m1
[M0L–1T0]
q1 q 2
4Fr 2
Permittivity of free
space (0)
0 
Dielectric constant
(K)
K=
Capacitance (C)
Charge
P.D.
Coefficient of self
induction (L)
L=
Coefficient of mutual
inductance (M)
ed t
dI
Magnetic flux ()
d =
Magnetic induction
(B)
Magnetic dipole
moment (M)

0
(w / q)dt
dI
M = IA
4r Fr 2
m1m 2
Permeability of free
space (0)
0 =
Rydberg constant (R)
22 mk 2 e 4
ch 3
5
Std. XI : Triumph Physics

Quantities having same dimensions:
Dimension
0 0 –1
[M L T ]
[M1L2T–2]
[M1L–1T–2]
[M1L1T–1]
[M0L1T–2]
[M1L1T–2]
[M1L2T–1]
[M1L0T–2]
[M0L0T0]
[M0L2T–2]
[ML2T–2–1]
[M0L0T1]
[M0L0T1]
[ML2T–2]

Quantity
Frequency, angular frequency, angular velocity, velocity gradient and decay
constant
Work, internal energy, potential energy, kinetic energy, torque, moment of force
Pressure, stress, Young’s modulus, bulk modulus, modulus of rigidity, energy
density
Momentum, impulse
Acceleration due to gravity, gravitational field intensity
Thrust, force, weight, energy gradient
Angular momentum and Planck’s constant
Surface tension, Surface energy (energy per unit area), spring constant
Strain, refractive index, relative density, angle, solid angle, distance gradient,
relative permittivity (dielectric constant), relative permeability etc.
Latent heat and gravitational potential
Thermal capacity, gas constant, Boltzmann constant and entropy
l / g , m / k , R / g , where l = length
g = acceleration due to gravity, m = mass, k = spring constant,
R = Radius of earth
L/R, LC , RC where L = inductance, R = resistance, C = capacitance
V2
q2
t, VIt, qV, LI2,
, CV2
R
C
where I = current, t = time, q = charge, L = inductance, C = capacitance,
R = resistance
I2Rt,
A few quick conversions:
i.
Pressure:
1 N/m2 = 10 dyne/ cm2 or
1 dyne/cm2 = 0.1 N/m2.
ii.
iii.
iv.
v.
6

To express large or small magnitudes
following prefixes are used:
Prefix
Symbol
10
18
exa
E
10
15
peta
P
10
12
tera
T
10
9
giga
G
10
6
mega
M
10
3
kilo
k
10
2
hecta
h
10
deca
da
Magnetic induction:
S I unit is tesla (Wb/m2) and CGS unit is
Gauss.
1 gauss = 104 tesla or
1 tesla = 104 gauss.
101
deci
d
10
2
centi
c
10
3
milli
106
micro
m

Magnetic flux:
SI unit is weber and CGS unit is
maxwell.
1 Wb = 108 maxwell or
1 maxwell = 108 Wb.
9
nano
n
12
pico
p
femto
f
atto
a
Density:
1 kg/m3 = 103 g/cm3 or
1 g/cm3 = 103 kg/m3.
Coefficient of viscosity:
SI units is decapoise (N s/m2) and CGS
unit is poise.
1 poise = 101 decapoise or
1 decapoise = 10 poise.
Power of 10
10
10
1015
10
18
Chapter 01: Measurements
1.4
Classical Thinking
1.0
1.
2.
Nano size of gold has _______ colour.
(A) yellow
(B) red
(C) pink
(D) orange
3.
Maxwell’s equations relate to _______.
(A) law of gravitation
(B) basic laws of electromagnetism
(C) laws of electrostatics
(D) nuclear model of an atom
1.1
4.
6.
S.I system of unit contains
supplementary unit.
(A) 7
(B) 2
(C) many
(D) 4
11.
In which of following system, scientific data
can be exchanged between different parts of
the world?
(A) M.K.S.
(B) C.G.S.
(C) F.P.S.
(D) S.I.
1.5
Need for measurements
Units of measurements
The reference standard used for the
measurement of a physical quantity is called
_______.
(A) standard quantity (B) dimension
(C) constant
(D) unit
Which of the following
characteristic of a good unit?
(A) It is invariable.
(B) It is reproducible.
(C) It is perishable.
(D) It is easily available.
1.3
is
NOT
7.
Units are classified into ______ groups.
(A) 2
(B) 4
(C) 5
(D) 6
8.
A set of fundamental and derived units is
known as _______.
(A) supplementary units
(B) system of units
(C) complementary units
(D) metric units
9.
The physical quantity having the same unit in
all the systems of unit is _______.
(A) length
(B) time
(C) mass
(D) foot
Fundamental and derived units
Out of the following units, which is NOT a
fundamental unit?
(A) newton
(B) second
(C) pound
(D) kg
13.
Temperature can be expressed as a derived
quantity in terms of
(A) length and mass
(B) mass and time
(C) length, mass and time
(D) none of these
14.
Which of the following is NOT a derived unit?
(A) joule
(B) erg
(C) dyne
(D) mole
15.
Which of the following is the CORRECT way
of writing units?
(A) 25 ms length
(B) 30 Kg
(C) 5 Newton
(D) 10 N
16.
To measure the distance of a planet from the
earth ______ method is used.
(A) echo
(B) direct
(C) parallax
(D) paradox
17.
The mass of the body depends only on
(A) temperature.
(B) pressure.
(C) quantity of matter contained in the body.
(D) location of the body from the observer.
18.
Which of the following represents a unified
atomic mass unit (1u)?
(A) 8.333  101 of the mass of an atom of
12
C in kg
(B) 0.8333  101 of the mass of an atom of
12
C in g
(C) 8.333  101 of the mass of an atom of
12
C in g
(D) 0.8333  101 of the mass of an atom of
12
C in kg
a
System of units
_______
12.
_______ is needed for the experimental
verification of various theories.
(A) Unit
(B) Symbol
(C) Instrument
(D) Measurement
1.2
5.
10.
Introduction
The atomic, molecular and nuclear phenomena
are the parts of ______ domain.
(A) macroscopic
(B) microscopic
(C) megascopic
(D) electroscopic
S.I Units
7
Std. XI : Triumph Physics
30.
A ______ is the interval from one noon to the
next noon.
(A) mean solar day (B) solar day
(C) lunar day
(D) day
Which of the following is NOT
dimensionless quantity?
(A) angle
(B) strain
(C) specific gravity (D) density
31.
Light year is a unit for the measurement of
_______.
(A) distance
(B) time
(C) temperature
(D) luminous intensity
The unit of plane angle is radian, hence its
dimensions are
(A) [M0L0T0]
(B) [M1L1T0]
0 1 1
(D) [M1L0T1]
(C) [M L T ]
32.
Dimensional equation CANNOT be used
(A) to check the correctness of a physical
quantity.
(B) to derive the relation between different
physical quantities.
(C) to find out constant of proportionality
which may be pure number.
(D) to change from one system of units to
another system.
33.
If the dimensional formula for the physical
quantity is [M1L2T2] then the physical
quantity is _______.
(A) torque
(B) impulse
(C) force
(D) force per unit area
34.
If the dimensions of a physical quantity are
given by [LaMbTc], then the physical quantity
will be
(A) force, if a = 1, b = 0, c = 2
(B) pressure, if a = 1, b = 1, c = 2
(C) velocity, if a = 1, b = 0, c = 1
(D) acceleration, if a = 1, b = 1, c = 2
19.
In cesium atomic clock ______ is used.
(A) cesium-122 atom (B) cesium-132 atom
(C) cesium-133 atom (D) cesium-134 atom
20.
21.
22.
Which of the following quantity is expressed
as force per unit area?
(A) work
(B) pressure
(C) volume
(D) density
23.
The physical quantity having the unit dyne g1
is _______.
(A) velocity
(B) mass
(C) force
(D) acceleration
24.
The SI unit of luminous intensity is _______.
(A) watt
(B) lux
(C) lumen
(D) candela
25.
Which of the following is a supplementary unit?
(A) steradian
(B) candela
(C) kelvin
(D) pascal
26.
3
The pressure of 10 dyne/cm is equivalent to
(B) 102 N/m2
(A) 10 N/m2
2
2
(D) 101 N/m2
(C) 10 N/m
1.6
27.
28.
29.
8
2
Dimensional analysis
[M1L1T2] is the dimensional formula for
_______.
(A) joule constant
(B) gravitational constant
(C) pressure
(D) force
Checking the correctness of physical
equations using the method of dimensions is
based on
(A) equality of inertial frame of reference.
(B) the type of system of units.
(C) the method of measurement.
(D) principle of homogeneity of dimensions.
A unitless quantity
(A) always has a non-zero dimension.
(B) may have a non-zero dimension.
(C) never has a zero dimension.
(D) has no dimensions.
1.7
a
Order of magnitude and significant
figures
35.
The value of the magnitude rounded off to the
nearest integral power of 10 is called _______.
(A) significant figure
(B) uncertain number
(C) significant number
(D) order of magnitude
36.
Order of magnitude of (106 + 103) is
(B) 109
(A) 1018
6
(D) 103
(C) 10
37.
The length of a rod is 0.5  102 m, the order of
magnitude of the length of the rod is
(B) 102 m
(A) 103 m
(C) 101 m
(D) 101 m
Chapter 01: Measurements
38.
The charge on the electron is 1.6  1019 C.
The order of magnitude is
(B) 1018 C
(A) 1019 C
(C) 1018 C
(D) 1019 C
39.
Significant figures depends upon the ______
of the measuring instrument.
(A) length
(B) readings
(C) number
(D) accuracy
40.
The number of significant figures in 0.0009 is
(A) 4
(B) 3
(C) 2
(D) 1
41.
The number of significant figures in 0.400 is
(A) 1
(B) 2
(C) 3
(D) 4
42.
The number of significant figures in 0.0500 is
(A) 4
(B) 3
(C) 2
(D) 1
43.
State the number of significant figures in
6.032 J
(A) 4
(B) 3
(C) 2
(D) 1
1.8
44.
45.
49.
Error due to non-removal of parallax between
pointer and its image in case of magnetic
compass needle causes _______.
(A) instrumental error
(B) persistant error
(C) personal error
(D) random error
50.
Instrumental error can be minimised by
(A) taking large number of readings.
(B) using different accurate instrument for
the same reading.
(C) adjusting zero of the instrument.
(D) maintaining the temperature of the
surrounding.
51.
The magnitude of the difference between
mean value and each individual value is called
_______.
(A) absolute error
(B) error in reading
(C) most probable error
(D) true error
52.
The formula for percentage error is
a m
 100%
(A) Percentage error =
am
Accuracy and errors in measurements
The difference between the true value and
measured value is called _______.
(A) mistake
(B) error
(C) significant figures (D) fault
If the pointer of the voltmeter is not exactly at
the zero of the scale then the error is called
_______.
(A) instrumental error (B) systematic error
(C) personal error
(D) random error
46.
Zero error of an instrument introduces
(A) systematic error
(B) random error
(C) instrumental error
(D) none of these
47.
Accidental error can be minimised by
(A) taking only one reading.
(B) taking small magnitude of the quantity.
(C) selecting instrument with greater least count.
(D) selecting instrument with small least count.
48.
Constant error can be caused due to
(A) faulty construction of instrument.
(B) wrong setting of instrument.
(C) lack of concentration of observer.
(D) wrong procedure of handling
instrument.
the
(B)
(C)
(D)
1 n
 a i  100%
n i1
a
Percentage error = m  100%
a m
Percentage error =
n
Percentage error = 1  ai  100%
n i1
a
, then maximum relative error in the
b
measurement is
a / a
a b
(A)

(B)
b / b
a
b
a b
b / b

(D)
(C)
a / a
a
b
53.
If x =
54.
Given: l1 = 44.2  0.1 and l2 = 23.1  0.1, the
uncertainty in l1 + l2 is
(A) 0
(B) 0.1
(C) 0.2
(D) 0.4
55.
Two resistances R1 = 50  2 ohm and
R2 = 60  3 ohm are connected in series, the
equivalent resistance of the series combination
is
(B) (110  2) ohm
(A) (110  4) ohm
(D) (110  6) ohm
(C) (110  5) ohm
9
Std. XI : Triumph Physics
56.
57.
If x = an then relative error is (where n is
power of a)
a
a
+n
(B) n
(A)
a
a
a
a
n
(D)
(C)
a
na
Thickness of the paper measured by
micrometer screw gauge of least count
0.01 mm is 1.03 mm, the percentage error in
the measurement of thickness of paper is
(A) 1.1%
(B) 1%
(C) 0.97%
(D) 0.8%
Critical Thinking
1.2
1.
Miscellaneous
58.
One micron is related to centimetre as
(A) 1 micron = 108 cm
(B) 1 micron = 106 cm
(C) 1 micron = 105 cm
(D) 1 micron = 104 cm
10
System of units
Which of the following system of units is not
based on units of mass, length and time alone?
(A) S.I.
(B) M.K.S
(C) F.P.S
(D) C.G.S
1.5
Fundamental and derived units
3.
The physical quantity denoted by
mass  pressure
is _______.
density
(A) force
(B) momentum
(C) angular momentum (D) work
4.
Universal time is based on
(A) rotation of the earth on its axis.
(B) Earth’s orbital motion around the Sun.
(C) vibrations of cesium atom.
(D) oscillations of quartz crystal.
5.
1 a.m.u. is equivalent to
(A) 1.6  1027 kg
(B)
24
(D)
(C) 1.6  10 g
Electronic analytical balance
An analytical balance is a balance designed to
measure small mass in the sub-milligram range. The
measuring pan (0.1 mg) is inside a transparent
enclosure with doors so that dust does not collect
and air currents in the room do not affect the
balance's operation.
Electronic analytical scale measures the force
needed to counter the mass being measured rather
than using actual masses.
If u1 and u2 are the units selected in two
systems of measurement and n1 and n2 are
their numerical values, then
(B) n1u1 + n2u2 = 0
(A) n1u1 = n2u2
(D) (n1+ u1) = (n2 + u2)
(C) n1n2 = u1u2
1.3
2.
Units of measurements
934 MeV
All of the above
6.
The S.I. unit of momentum is
kg
kg m
(A)
(B)
m
s
kg m 2
(C)
(D) kg  newton
s
7.
Curie is a unit of
(A) energy of -rays
(B) half life
(C) radioactivity
(D) intensity of -rays
8.
S = A(1  eBxt), where S is speed and x is
displacement. The unit of B is
(A) m1s1
(B) m2s
(C) s2
(D) s1
Chapter 01: Measurements
9.
10.
11.
To determine the Young’s modulus of a wire,
F L
the formula is Y = ´
; where L = length,
A DL
A = area of cross-section of the wire, L =
change in length of the wire when stretched
with a force F. The conversion factor to
change it from CGS to MKS system is
(A) 1
(B) 10
(C) 0.1
(D) 0.01
The moon subtends an angle of 57 minute at
the base-line equal to the radius of the earth.
What is the distance of the moon from the
earth? [Radius of the earth = 6.4  106 m]
(A) 11.22  108 m
(B) 3.86  108 m
3
(C) 3.68  10 cm (D) 3.68  108 cm
The angular diameter of the sun is 1920. If
the distance of the sun from the earth is
1.5  1011 m, then the linear diameter of the
sun is
(A) 2.6  109 m
(B) 0.7  109 m
(D) 1.4  109 m
(C) 5.2  109 m
1.6
12.
17.
If the magnitude of length is halved and that
of mass is doubled then dimension of force is
(B) [M2L1/2T2]
(A) [M2L2T2]
(D) [M1L1T2]
(C) [M2L1/2T2]
18.
Out of the following pairs, which one does
NOT have identical dimensions?
(A) Energy and moment of force
(B) Work and torque
(C) Density and surface energy
(D) Pressure and stress
19.
Which of the following equations is
dimensionally correct?
(A) pressure = Energy per unit volume
(B) pressure = Energy per unit area
(C) pressure = Momentum  volume  time
(D) pressure = Force  area
20.
The dimensional formula for impulse is the
same as dimensional formula for _______.
(A) acceleration
(B) force
(C) momentum
(D) rate of change in momentum
21.
The dimensions of
Dimensional analysis
The fundamental physical quantities that have
same dimensions in the dimensional formulae
of torque and angular momentum are
(A) mass, time
(B) time, length
(C) mass, length
(D) time, mole
13.
Which of the following represents correct
dimensions of the coefficient of viscosity?
(A) [M1L1T2]
(B) [M1L1T1]
1 1 1
(D) [M1L2T2]
(C) [M L T ]
14.
The dimensional equation for the electrical
resistance of a conductor is
(A) [M1L2T2I1]
(B) [M1L2T2I1]
1 1 3 2
(C) [M L T I ]
(D) [M1L2T3I2]
15.
Dimensions of length in electric dipole
moment, electric flux and electric field are
respectively
(A) L, L2, L3
(B) L3, L2, L
1
3
3
(D) L, L3, L
(C) L , L , L
16.
If L denotes the inductance of an inductor
through which a current i is flowing, the
dimensions of Li2 are
(A) [L2M1T2]
(B) Not expressible in LMT
(C) [L1M1T2]
(D) [L2M2T2]
(A)
(C)
Velocity
Capacitance
1
is that of
00
(B)
(D)
Time
Distance
22.
Which of the following pair has same
dimensions?
(A) Current density and charge density
(B) Angular momentum and momentum
(C) Spring constant and surface energy
(D) Force and torque
23.
The terminal velocity v of a small steel ball of
radius r falling under gravity through a
column of viscous liquid coefficient of
viscosity  depends on mass of the ball m,
acceleration due to gravity g. Which of the
following relation is dimensionally correct?
mgr
(B) v  mgr
(A) v 

mg
mg
(C) v 
(D) v 
r
r
24.
A force F is given by F = at + bt2, where ‘t’ is
time. What are the dimensions of a and b?
(A) [M1L1T1] and [M1L1T0]
(B) [M1L1T3] and [M1L1T4]
(C) [M1L1T4] and [M1L1T1]
(D) [M1L3T1] and [M1L1T4]
11
Std. XI : Triumph Physics
25.
The force F is expressed in terms of distance x and
time t as F = a x + bt2. The dimensions of a/b is
(A) [M0L0T2]
(B) [M0L1/2T2]
(C) [M0L1/2T2]
(D) [M0L1/2T2]
26.
For the equation F  Aa vb dc, where F is the
force, A is the area, v is the velocity and d is the
density, the values of a, b and c are respectively
(A) 1, 2, 1
(B) 2, 1, 1
(C) 1, 1, 2
(D) 0, 1, 1
27.
28.
29.
Using the principle of homogeneity of
dimensions, find which of the following relation
is correct? [T is the time period, a is the radius of
the orbit and M is the mass of the sun.]
42 a 3
42 a 3
(B) T2 =
(A) T2 =
G
GM
4
2 a 3
(D) T2 =
(C) T2 = 42a3
GM 2
The period of a body under SHM is
represented by T = PaDbSc ; where P is
pressure, D is density and S is surface tension.
The value of a, b and c are
3 1
(B) 1, 2, 3
(A)  , , 1
2 2
1
3 1
1
,  
(D) 1, 2,
(C)
2
2 2
3
The equation of a wave is given by
æx
ö
Y = A sin  çç - k ÷÷÷
çè v
ø
where  is the angular velocity and v is the
linear velocity. The dimension of k is
(A) LT
(B) T
(D) T2
(C) T1
30.
Find the dimensions of (a/b) in the equation:
a  t2
P=
bx
Where P is pressure, x is distance and t is time.
(B) [M1L0T2]
(A) [M1L1T2]
1 2 2
(D) [M1L2T2]
(C) [M L T ]
31.
The equation of state of some gases can be
a 

expressed as  P  2  (V  b) = RT. Here P is
V 

the pressure, V is the volume, T is the absolute
temperature and a, b, R are constants. The
dimensions of ‘
(A)
(C)
12
a
’ are
b
[M1L2T2]
[M0L3T0]
(B)
(D)
[ML1T2]
[M0L6T0]
32.
If the speed of light (c), acceleration due to
gravity (g) and pressure (p) are taken as the
fundamental quantities, then the dimension of
gravitational constant is
(B) [c0g2p1]
(A) [c2g0p2]
3 2
(C) [cg p ]
(D) [c1g0p1]
33.
The value of acceleration due to gravity is
980 cm s2. If the unit of length is kilometre
and that of time is minute then value of
acceleration due to gravity is
(B) 98 km min2
(A) 980 km min2
(C) 35.28 km min2 (D) 28.35 km min2
1.7
Order of magnitude and significant
figures
34.
The magnitude of any physical quantity can be
expressed as A  10n where n is a number
called order of magnitude and A is
(B) 0.5  A < 5
(A) 0.1  A < 1
(C) 5  A < 9
(D) 1  A > 9
35.
The radius of the earth is 6400 km, the order
of magnitude is
(A) 107 m
(B) 104 m
3
(D) 102 m
(C) 10 m
36.
The order of magnitude of 49 and the order of
magnitude of 51
(A) is same.
(B) differs by 1.
(C) is 1.
(D) is 2.
37.
Calculate the number of seconds in a day and
express it in the order of magnitude.
(A) 8.64 104 s, 105 s (B) 6.84 104 s, 104 s
(C) 8.64 105 s, 105 s (D) 6.85 104 s, 105 s
38.
Figure which is of some significance but it
does not necessarily denote certainty is
defined as _______.
(A) special figures
(B) characteristic figures
(C) unknown figures
(D) significant figures
39.
The number of significant figures in all the
given numbers 25.12, 2009, 4.156 and
1.217  104 is
(A) 1
(B) 2
(C) 3
(D) 4
40.
The answer of (9.15 + 3.8) with due regards
to significant figure is
(A) 13.000
(B) 13.00
(C) 13.0
(D) 13
Chapter 01: Measurements
41.
In the reading 2.614 cm of measurement with
a vernier calliper, only uncertain figure is
(A) 1
(B) 2
(C) 4
(D) 6
42.
The sides of a rectangle are 6.01 m and 12 m.
Taking the significant figures into account, the
area of the rectangle is
(B) 72.1 cm2
(A) 72.00 cm2
2
(D) 72.12 cm2
(C) 72 m
1.8
43.
44.
48.
The percentage error in the measurement of
mass of a body is 0.75% and the percentage
error in the measurement of its speed is
1.85%. Then the percentage error in the
measurement of its kinetic energy is
(A) 7.05%
(B) 4.45%
(C) 2.6%
(D) 1.1%
49.
The error in the measurement of length (L) of
the simple pendulum is 0.1% and the error in
time period (T) is 3%. The maximum possible
L
error in the measurement of 2 is
T
(A) 2.9%
(B) 3.1%
(C) 5.9%
(D) 6.1%
50.
The period of oscillation of a simple pendulum
l
where l is about
is given by T = 2
g
100 cm and is known to have 1 mm accuracy.
The period is about 2 s. The time of
100 oscillations is measured by a stop watch of
least count 0.1 s. The percentage error in g is
(A) 0.1%
(B) 1%
(C) 0.3%
(D) 0.8%
51.
The length, breadth and height of a rectangular
block of wood were measured to be
l = 13.12  0.02 cm, b = 7.18  0.01 cm,
h = 4.16  0.02 cm.
The percentage error in the volume of the
block will be
(A) 7%
(B) 0.77%
(C) 0.72%
(D) 0.27%
52.
The heat dissipated in a resistance can be
I 2 Rt
determined from the relation: H =
cal
4.2
If the maximum errors in the measurement of
current, resistance and time are 2%, 1% and
1% respectively, what would be the maximum
error in the dissipated heat?
(A) 5%
(B) 4%
(C) 6%
(D) 0.5%
Accuracy and errors in measurements
Estimate the mean absolute error from the
following data.
20.17, 21.23, 20.79, 22.07, 21.78
(A) 0.85
(B) 0.58
(C) 0.03
(D) 0.01
In the expression A =
xy3
the percentage
z2
error is given by
45.
(A)
 x
y
z 
3
 2  100%

y
z 
 x
(B)
 x 3y 2z 



  100%
y
z 
 x
(C)
 x 3y 2z 



  100%
y
z 
 x
(D)
 x
y
z 
3
 2  100%

y
z 
 x
The least count of a screw gauge is 0.005 cm.
The diameter of a wire is 0.020 cm as measured
by it. The percentage error in measurement is
(A) 25%
(B) 20%
(C) 15%
(D) 5%
46.
The percentage error in the measurement of
radius r of a sphere is 0.1% then the percentage
error introduced in the measurement of volume
is
(A) 0.1%
(B) 0.2%
(C) 0.25%
(D) 0.3%
47.
The pressure on a square plate is measured by
measuring the force on the plate and the length
of the sides of the plate. If the maximum error
in the measurement of force and length are
respectively 4% and 2%, The maximum error
in the measurement of pressure is
(A) 1%
(B) 2%
(C) 6%
(D) 8%
Miscellaneous
53.
If momentum (P), area (A) and time (T) are
assumed to be fundamental quantities, then
energy has dimensional formula
(A) [P1A1/2T1]
(B) [P1A1/2T1]
(D) [P1A1T1]
(C) [P2A1T1]
13
Std. XI : Triumph Physics
54.
Assertion: Avogadro number is the number of
atoms in one gram mole.
Reason: Avogadro number is a dimensionless
constant.
55.
(A)
Assertion is True, Reason is True; Reason
is a correct explanation for Assertion
(B)
Assertion is True, Reason is True; Reason
is not a correct explanation for Assertion
(C)
Assertion is True, Reason is False
(D)
Assertion is False, Reason is False.
Competitive Thinking
1.5
1.
(A)
Assertion is True, Reason is True; Reason
is a correct explanation for Assertion
(B)
Assertion is True, Reason is True; Reason
is not a correct explanation for Assertion
(C)
Assertion is True, Reason is False
(D)
Assertion is False, Reason is False.
14
Jm
(D)
J
m2
2.
Which of the following is not the unit of
energy?
[MP PET 1998, 2000]
(A) watt-hour
(B) electron volt
(C) N m
(D) kg m2 s2
3.
Units of ‘a’ in Van der Waals equation of state
is
[MH CET 2002]
(A) Nm4/mole.
(B) Nm2/mole.
(D) none of these.
(C) N2m/mole.
4.
Unit of constant b in Van der Waal’s equation
is
[MH CET 2006]
(A) m3/mole
(B) m2/mole
(C) m/mole
(D) m3
5.
The S.I. units of the constant in Wein’s
displacement law are
[MH CET 2008; 2009]
1
(B) mK
(A) cm K
(C) cm2K1
(D) cm K2
6.
S. I unit of principle specific heat is
[MH CET 2004]
(A) kcal/gm K
(B) cal/gm K
(C) J/kg K
(D) erg/kg K
7.
As is unit of
(A) capacitance.
(C) energy.
8.
S.I. unit of specific resistance is
[MH CET 2004]
(B)  m
(A)  cm
(D) mho-cm
(C) /cm
9.
The unit of permeability of vacuum (μ0) is
_____.
[GUJ CET 2014]
N
N
(A)
(B)
A
A2
J
(C) NA
(D)
A2
10.
1 Tesla =
(A) 1 Wb/m
(C) 1 N/Am
Quartz crystal clock
A quartz clock is a clock that uses an electronic
oscillator regulated by a quartz crystal to keep time.
This crystal oscillator creates a signal with very
precise frequency, so that clock has an accuracy of
1 s in every 109 s.
Correct unit of surface tension is
[MH CET 2011]
J
N
(B)
(A)
2
m
m
(C)
Assertion: The graph between P and Q is
straight line, when P/Q is constant.
Reason: The straight line graph means that P
is proportional to Q or P is equal to constant
multiplied by Q.
Fundamental and derived units
[MH CET 2002]
(B) charge.
(D) power.
(B)
(D)
[MH CET 2004]
1 J/Am
1 Am/N
Chapter 01: Measurements
11.
Unit of ‘’ in radioactivity is
(A)
(C)
12.
13.
15.
16.
17.
(B)
(D)
Dimension’s of planck’s constant are same as
the dimensions of the product of
[MH CET 2010]
(A) Force and time
(B) Force, displacement and time.
(C) Force and velocity
(D) Force and displacement
19.
Which of the following set have different
dimensions?
[IIT 2005]
(A) Pressure, Young’s modulus, stress
(B) e.m.f, potential difference, electric potential
(C) Heat, work done, energy
(D) dipole moment, electric flux, electric
field
20.
The dimensions of G, the gravitational
constant, are
[AIIMS 2000; MH CET 2006;
Orissa JEE 2010; BCECE 2015]
(B) [ML3T2]
(A) [MLT2]
(D) [M1LT2]
(C) [M1L3T2]
21.
Dimension of angular momentum is
[MH CET 2004]
(A) [M1L2T–2]
(B) [M1L–2T–1]
(C) [M1L2T–1]
(D) [M1L0T–1]
22.
Dimension of surface tension is
[MH CET 2002]
1 2 2
(A) [M L T ]
(B) [M1L0T2]
(C) [M1L2T2]
(D) [M0 L0 T2]
23.
Dimension of force constant is given by,
[MH CET 2003]
(A) [M1L1T–2]
(B) [M0L1T–1]
(C) [M1L0T–2]
(D) [M1L0T–1]
24.
The dimensions of K in the equation
1
[Orissa JEE 2003]
W = Kx 2 is
2
(A) [M1L0T2]
(B) [M0L1T1]
1 1 2
(D) [M1L0T1]
(C) [M L T ]
25.
An object is moving through the liquid. The
viscous damping force acting on it is
proportional to the velocity. Then dimension
of constant of proportionality is
[Orissa JEE 2002]
(B) [M1L1T1]
(A) [M1L1T1]
(D) [M1L0T1]
(C) [M0L1T1]
26.
The dimensional formula for Reynold’s
number is
[MH CET 2014]
(A) [L0 M0 T0]
(B) [L1 M1 T1]
(C) [L1 M1 T1]
(D) [L1 M1 T1]
[MH CET 2002]
(unit of half life)–1
sec
If the unit of length and force be increased
four times, then the unit of energy is
[Kerala PMT 2005]
(A) increased 4 times.
(B) increased 8 times.
(C) increased 16 times.
(D) decreased 16 times.
The surface tension of a liquid is 108 dyne/cm.
It is equivalent to
[MH CET 1999]
7
(A) 10 N/m
(B) 106 N/m
(D) 104 N/m
(C) 105 N/m
1.6
14.
m
(year)–1
18.
Dimensional analysis
L
The quantities RC and   (where R, L and
R
C stand for resistance, inductance and
capacitance respectively) have the dimensions
of
[Kerala PET 2010]
(A) force
(B) linear momentum
(C) linear acceleration(D) time
R, L and C represent the physical quantities
resistance, inductance and capacitance
respectively. Which one of the following
combination has dimensions of frequency?
[IIT JEE 1986]
R
R
(B)
(A)
L
RC
1
C
(D)
(C)
LC
L
0 LV
:0 is the permittivity
t
of free space, L is length, V is potential
difference and t is time. The dimensions of X
are same as that of
[IIT JEE 2001; AMU (Engg.) 2009]
(A) Resistance
(B) Charge
(C) Voltage
(D) Current
The quantity X 
Planck’s constant has same dimensions as
[MH CET 2004]
(A) energy.
(B) angular momentum.
(C) mass.
(D) force.
15
Std. XI : Triumph Physics
27.
The dimensions of universal gas constant is
[Pb PET 2003; AIIMS 2010]
2 2 1
(B) [M2LT2θ]
(A) [ML T θ ]
(D) None of these
(C) [ML3T1θ1]
28.
The relation between force ‘F’ and density ‘d’
x
is F =
. The dimensions of x are
d
[MH CET 2014]
29.
(A)
[L1/ 2 M 3/2 T 2 ]
(B)
[L1/ 2 M1/2 T 2 ]
(C)
[L1 M 3/ 2 T 2 ]
(D)
[L1 M1/ 2 T 2 ]
31.
32.
33.
16
The dimensional formula of magnetic flux is
_______.
[MH CET 2001, GUJ CET 2014]
1 2 3 1
(B) [M1L2T–2A–1]
(A) [M L T A ]
(C) [M1L2T2A1]
(D) [M1L3T2A1]
35.
The dimensions of solar constant are
[BCECE 2015]
36.
Force F is given by the equation
X
F=
. Then dimensions of X are
Linear density
(A)
(C)
30.
34.
[TS EAMCET (Engg.) 2015]
(B) [M0L0T1]
[M L T ]
[L2T2]
(D) [M0L2T2]
2 0 2
What is dimension of a in Van der Waal’s
equation?
[MH CET 2005]
1 1 2
2
(A) [M L T mol ]
(B) [M1L3T2mol2]
(C) [M1L5T2mol2]
(D) [M1L3T2mol1]
Let [0] denote the dimensional formula of
the permittivity of vacuum. If M = mass,
L = length, T = time and A = electric current,
then
[JEE (Main) 2013]
–1 –3 2
(A) [0] = [M L T A]
(B) [0] = [M–1 L–3 T4 A2]
(C) [0] = [M–1 L2 T–1 A–2]
(D) [0] = [M–1 L2 T–1 A]
Dimensional formula for electrical field is
_______ .
[GUJ CET 2014]
1 2 3 2
(A) [M L T A ]
(B) [M1L2T3A1]
1 1 3 1
(C) [M L T A ]
(D) [M0L0T0A0]
1
 E2, where 0 is
2 0
permittivity of free space and E is electric
field, is
[AIPMT 2010]
2 1 2
(A) [L M T ]
(B) [L1M1T2]
2 1 2
(D) [L1M1T1]
(C) [L M T ]
The dimension of
(A)
[MLT2]
(B)
[M0L0T0]
(C)
[ML0T3]
(D)
[M0LT3]
The velocity v of a particle at time t is given
b
, where a, b and c are
by v = at +
tc
constants. The dimensions of a, b and c are
respectively
[AIPMT 2006]
2
(A) L, LT and T
(B)
(C)
(D)
LT2, L and T
L2,T and LT2
LT2, LT and L
37.
If E, M, J and G respectively denote energy,
mass, angular momentum and gravitational
EJ 2
constant, then 5 2 has the dimensions of
MG
[AIIMS 1985; IIT 1990]
(A) length
(B) angle
(C) mass
(D) time
38.
If X = 3YZ2 then the dimension of Y in MKS
system, if X and Z are the dimension of
capacity and magnetic field respectively is
[MP PMT 2003]
39.
(A)
[M3L2T4A1]
(B)
[M1L2]
(C)
[M3L2T4A4]
(D)
[M3L2T8A4]
If the time period (T) of vibration of a liquid
drop depends on surface tension (S), radius (r)
of the drop and density () of the liquid, then
the expression of T is
[AMU (Med.) 2000]
(A)
T = k r 3 / S
(B)
T= k 1/ 2 r 3 / S
(C)
T = k r 3 / S1/ 2
(D)
T = None of these
Chapter 01: Measurements
40.
α
In the relation P = e
β
-α Z
kθ
P is pressure, Z is
45.
In an experiment the angles are required to be
measured using an instrument. 29 divisions of
the main scale exactly coincide with the 30
divisions of the vernier scale. If the smallest
division of the main scale is half-a-degree
(=0.5) then the least count of the instrument
is
[AIEEE 2009]
(A) one minute
(B) half minute
(C) one degree
(D) half degree
46.
A vernier callipers has 1 mm marks on the
main scale. It has 20 equal divisions on the
Vernier scale which match with 16 main scale
divisions. For this Vernier callipers, the least
count is
[IIT JEE 2010]
(A) 0.02 m
(B) 0.05 mm
(C) 0.1 mm
(D) 0.2 mm
47.
The diameter of a cylinder is measured using
a Vernier callipers with no zero error. It is
found that the zero of the Vernier scale lies
between 5.10 cm and 5.15 cm of the main
scale. The Vernier scale has 50 divisions
equivalent to 2.45 cm. The 24th division of
the Vernier scale exactly coincides with one
of the main scale divisions. The diameter of
the cylinder is
[JEE (Advanced) 2013]
(A) 5.112 cm
(B) 5.124 cm
(C) 5.136 cm
(D) 5.148 cm
48.
A student measured the length of a rod and
wrote it as 3.50 cm. Which instrument did he
use to measure it?
[JEE (Main) 2014]
(A) A metre scale
(B) A vernier calliper where the 10 divisions
in vernier scale matches with 9 division
in main scale and main scale has
10 divisions in 1 cm
(C) A screw gauge having 100 divisions in
the circular scale and pitch as 1 mm
(D) A screw guage having 50 divisions in
the circular scale and pitch as 1 mm
49.
In a vernier callipers, one main scale division
is x cm and n divisions of the vernier scale
coincide with (n – 1) divisions of the main
scale. The least count (in cm) of the callipers
is
[AMU PMT 2009]
nx
 n 1 
(B)
(A) 
x
(n 1)
 n 
the distance, k is Boltzmann’s constant and θ
is the temperature. The dimensional formula
[IIT (Screening) 2004]
of β will be
0 2 0
(B) [M1L2T1]
(A) [M L T ]
(D) [M0L2T1]
(C) [M1L0T1]
41.
Match the following two columns.
Column I
(a) Electrical
resistance
(b) Electrical potential
(c) Specific resistance
(d) Specific
conductance
Column II
(p) [M1L3T3A2]
(q) [ML2T3A2]
(r) [ML2T3A1]
(s) None of these
[GUJ CET 2015]
(A)
(B)
(C)
(D)
42.
a – q, b – s, c – r, d – p
a – q, b – r, c – p, d – s
a – p, b – q, c – s, d – r
a – p, b – r, c – q, d – s
Match the list-I with list-II
List-I
List-II
Boltzmann
(I) [ML0T0]
constant
Q Coefficient
of (II) [ML1T1]
viscosity
R Water equivalent (III) [MLT3K1]
S Coefficient
of (IV) [ML2T–2K1]
thermal
conductivity
[AP EAMCET (Engg.) 2016]
(A) P – III, Q – I, R – II, S – IV
(B) P – III, Q – II, R – I, S – IV
(C) P – IV, Q – II, R – I, S – III
(D) P – IV, Q – I, R – II, S – III
P
1.7
Order of magnitude and significant
figures
43.
The number of significant figures in 0.002305
is
[Kerala PET 2010]
(A) 6
(B) 4
(C) 7
(D) 2
44.
The respective number of significant figures
for the numbers 23.023, 0.0003 and 2.1  103
are
[AIEEE 2010]
(A) 4, 4, 2
(B) 5, 1, 2
(C) 5, 1, 5
(D) 5, 5, 2
(C)
x
n
(D)
x
(n 1)
17
Std. XI : Triumph Physics
50.
51.
A screw guage gives the following reading
when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions
The diameter of wire from the above data is
[AIEEE 2011]
(A) 0.52 cm
(B) 0.052 cm
(C) 0.026 cm
(D) 0.005 cm
A spectrometer gives the following reading
when used to measure the angle of a prism.
Main scale reading : 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale
corresponds to 0.5 degree. Total divisions on
the vernier scale is 30 and match with 29
divisions of the main scale. The angle of the
prism from the above data
[AIEEE 2012]
(A) 58.59 degree
(B) 58.77 degree
(C) 58.65 degree
(D) 59 degree
54.
55.
If x = (a – b), the maximum percentage error
in the measurement of x will be
[BCECE 2015]
(A)
b 
 a
 a  b  a  b   100
(B)
b 
 a
 a  b  a  b   100
(C)
 a  b 
 a  b   100
(D)
 a b 
 a  b   100
If radius of the sphere is (5.3  0.1) cm. Then
percentage error in its volume will be
[Pb PET 2000]
(A)
(B)
1.8
52.
53.
18
Accuracy and errors in measurements
Choose the INCORRECT statement out of the
following.
[AMU 2010]
(A) Every measurement by any measuring
instrument has some error.
(B) Every calculated physical quantity that
is based on measured values has some
error.
(C) A measurement can have more accuracy
but less precision and vice versa.
(D) The percentage error is different from
relative error.
Assertion: The error in the measurement of
radius of the sphere is 0.3%. The permissible
error in its surface area is 0.6%.
Reason: The permissible error is calculated by
A
4r
=
[AIIMS 2008]
the formula
A
r
(A) Assertion is True, Reason is True; Reason
is a correct explanation for Assertion
(B) Assertion is True, Reason is True; Reason
is not a correct explanation for Assertion
(C) Assertion is True, Reason is False
(D) Assertion is False, Reason is False.
100
5.3
1
100
× 0.01×
3
5.3
3 + 6.01×
(C)
 3× 0.1 
 5.3  ×100


(D)
0.1
×100
5.3
56.
Resistance of a given wire is obtained by
measuring the current flowing in it and the
voltage difference applied across it. If the
percentage errors in the measurement of the
current and the voltage difference are 3%
each, then error in the value of resistance of
the wire is
[AIEEE 2012]
(A) 6%
(B) Zero
(C) 1%
(D) 3%
57.
In an experiment four quantities a, b, c and d
are measured with percentage error 1%, 2%,
3% and 4% respectively. Quantity P is
calculated as follows:
P=
(A)
(C)
a 3b2
 % error in P is
cd
14%
7%
[NEET UG 2013]
(B) 10%
(D) 4%
Chapter 01: Measurements
58.
59.
Two full turns of the circular scale of a screw
gauge cover a distance of 1 mm on its main
scale. The total number of divisions on the
circular scale is 50. Further, it is found that the
screw gauge has a zero error of – 0.03 mm.
While measuring the diameter of a thin wire, a
student notes the main scale reading of 3 mm
and the number of circular scale divisions in
line with the main scale as 35. The diameter of
the wire is
[AIEEE 2008]
(A) 3.73 mm
(B) 3.67 mm
(C) 3.38 mm
(D) 3.32 mm
25
20
5
0
61.
of length L = 2 m and diameter d = 0.5 mm is
used. For a load M = 2.5 Kg, an extension l =
0.25mm in the length of the wire is observed.
Quantities d and l are measured using a screw
gauge and a micrometer, respectively. They
have the same pitch of 0.5 mm. The number
of divisions on their circular scale is 100. The
contributions to the maximum probable error
of the Y measurement are
[IIT JEE 2012]
(A) due to the errors in the measurements of
d and l are the same.
(B) due to the error in the measurement of d
is twice that due to the error in the
measurement of l.
(C) due to the error in the measurement of l
is twice that due to the error in the
measurement of d.
(D) due to the error in the measurement of d
is four times that due to the error in the
measurement of l.
[IIT JEE 2006]
O 30
10
(A)
2.25 mm
(B)
2.20 mm
(C)
1.20 mm
(D)
1.25 mm
A screw gauge with a pitch of 0.5 mm and a
circular scale with 50 divisions is used to
measure the thickenss of a thin sheet of
aluminium. Before starting the measurement,
it is found that when the two jaws of the screw
gauge are brought in contact, the 45th division
coincides with the main scale line and that the
zero of the main scale is barely visible. What
is the thickness of the sheet if the main scale
reading is 0.5 mm and the 25th division
coincides with the main scale line?
[JEE (Main) 2016]
(A) 0.80 mm
(B) 0.70 mm
(C) 0.50 mm
(D) 0.75 mm
The density of a solid ball is to be
determined in an experiment. The diameter
of the ball is measured with a screw gauge,
whose pitch is 0.5 mm and there are 50
divisions on the circular scale. The reading
on the main scale is 2.5 mm and that on the
circular scale is 20 divisions. If the
measured mass of the ball has a relative
error of 2%, the relative percentage error in
the density is
[IIT JEE 2011]
(A) 0.9%
(B) 2.4%
(C) 3.1%
(D) 4.2%
In the determination of Young’s modulus
4MLg 

Y 
 by using Searle’s method, a wire
ld 2 

The circular divisions of shown screw gauge
are 50. It moves 0.5 mm on main scale in one
rotation. The diameter of the ball is
O
60.
62.
63.
If the time period of a simple pendulum is
T = 2  l / g , then the fractional error in
acceleration due to gravity is
[Assam CEE 2015]
(A)
(C)
64.
4  2 l
T 2
l
T
2
l
T
(B)
l
T
2
l
T
(D)
None of these
A student measures the value of g with the
help of a simple pendulum using the formula
42 L
g=
. He measures length L with a metre
T2
scale having least count 1 mm and finds it
98.0 cm. The time period is measured with the
help of a watch of least count 0.1 s. The time
of 20 oscillations is found to be 40.0 s. The
error g in the measurement of g is (in m/s2).
[BCECE 2014]
(A)
 0.1

 0.1
9.68 
 98

(B)
1

9.68   0.1
 98

(C)
 0.1 0.1 

9.68 
 98 20 
(D)
1
1
9.68   
 98 20 
19
Std. XI : Triumph Physics
65.
66.
I
II
III
The period of oscillation of a simple
L
. Measured value of L
pendulum is T = 2
g
is 20.0 cm known to 1 mm accuracy and time
for 100 oscillations of the pendulum is found
to be 90 s using a wrist watch of 1 s
resolution. The accuracy in the determination
of g is
[JEE (Main) 2015]
(A) 2%
(B) 3%
(C) 1%
(D) 5%
Students I, II and III perform an experiment for
measuring the acceleration due to gravity (g)
using a simple pendulum. They use different
lengths of the pendulum and/or record time for
different number of oscillations. The
observations are shown in the table.
Least count for length = 0.1 cm
Least count for time = 0.1 s
Length of
the
pendulum
(cm)
64.0
64.0
20.0
Total time
Number of
for (n)
oscillation
oscillations
(n)
(s)
8
128.0
4
64.0
4
36.0
Time
period
(s)
69.
x2  b
, where P is power, x is distance
at
and ‘t’ time? [AP EAMCET (Med.) 2016]
(A) Power
(B) Surface tension
(C) Torsional constant
(D) Force
P =
70.
If force (F), velocity (V) and time (T) are
taken as fundamental units, then the
dimensions of mass are
[AIPMT 2014]
1
(A) [F V T ]
(B) [F V T2]
(C) [F V1 T1]
(D) [F V1 T]
71.
If energy (E), velocity (V) and time (T) are
chosen as the fundamental quantities, the
dimensional formula of surface tension will be
[AIPMT 2015]
(A) [E V–2 T–1]
(B) [E V–1 T–2]
(C) [E V–2 T–2]
(D) [E–2 V–1 T–3]
72.
If the velocity of surface wave (v) depends
upon surface tension (T), coefficient of
viscosity () and density (), then the
expression for v will be
[Assam CEE 2015]
16.0
16.0
9.0
If EI, EII and EIII are the percentage errors in g,
 g

i.e., 
 100  for students I, II and III,
 g

respectively,
[IIT JEE 2008]
(A) EI = 0
(B) EI is minimum
(C) EI = EII
(D) EII is maximum
Which of the following physical quantities
b
represent the dimensions of in the relation
a
(A)
T2

(B)
T

(C)

T2
(D)


Miscellaneous
67.
68.
20
One femtometer is equivalent to [DCE 2004]
(A)
1015 m
(B)
1015 m
(C)
1012 m
(D)
1012 m
Which of the following units denotes the
dimensions ML2/Q2 where Q denotes the
electric charge?
[AIEEE 2006]
(A) henry (H)
(B) H/m2
(C) weber (Wb)
(D) Wb/m2
73.
The ratio of the dimensions of Planck constant
and that of moment of inertia has the
dimensions of
[K CET 2015]
(A) angular momentum.
(B) time.
(C) velocity.
(D) frequency.
Chapter 01: Measurements
Answer Key
Classical Thinking
1.
11.
21.
31.
41.
51.
(B)
(D)
(A)
(A)
(C)
(A)
2.
12.
22.
32.
42.
52.
(C)
(A)
(B)
(C)
(B)
(A)
3.
13.
23.
33.
43.
53.
(B)
(D)
(D)
(A)
(A)
(B)
4.
14.
24.
34.
44.
54.
(D)
(D)
(D)
(B)
(B)
(C)
5.
15.
25.
35.
45.
55.
(D)
(D)
(A)
(D)
(B)
(C)
6.
16.
26.
36.
46.
56.
(C)
(C)
(B)
(C)
(A)
(B)
7.
17.
27.
37.
47.
57.
(A)
(C)
(C)
(B)
(D)
(C)
8.
18.
28.
38.
48.
58.
(B)
(D)
(D)
(D)
(A)
(D)
9.
19.
29.
39.
49.
(B)
(C)
(D)
(D)
(C)
10.
20.
30.
40.
50.
(B)
(B)
(D)
(D)
(B)
3.
13.
23.
33.
43.
53.
(D)
(B)
(C)
(C)
(B)
(B)
4.
14.
24.
34.
44.
54.
(C)
(D)
(B)
(B)
(B)
(C)
5.
15.
25.
35.
45.
55.
(D)
(D)
(C)
(A)
(A)
(A)
6.
16.
26.
36.
46.
(B)
(A)
(A)
(B)
(D)
7.
17.
27.
37.
47.
(C)
(D)
(B)
(A)
(D)
8.
18.
28.
38.
48.
(A)
(C)
(A)
(D)
(B)
9.
19.
29.
39.
49.
(C)
(A)
(B)
(D)
(D)
10.
20.
30.
40.
50.
(B)
(C)
(B)
(C)
(C)
(D)
(C)
(C)
(B)
(B)
(C)
(C)
(D)
4.
14.
24.
34.
44.
54.
64.
(A)
(D)
(A)
(B)
(B)
(B)
(A)
5.
15.
25.
35.
45.
55.
65.
(B)
(B)
(D)
(C)
(A)
(C)
(B)
6.
16.
26.
36.
46.
56.
66.
(C)
(D)
(A)
(B)
(D)
(A)
(C)
7.
17.
27.
37.
47.
57.
67.
(B)
(B)
(A)
(B)
(B)
(A)
(B)
8.
18.
28.
38.
48.
58.
68.
(B)
(B)
(A)
(D)
(B)
(C)
(A)
9.
19.
29.
39.
49.
59.
69.
(B)
(D)
(A)
(A)
(C)
(C)
(C)
10.
20.
30.
40.
50.
60.
70.
(C)
(C)
(C)
(A)
(B)
(A)
(D)
Critical Thinking
1.
11.
21.
31.
41.
51.
(A)
(D)
(A)
(A)
(C)
(B)
2.
12.
22.
32.
42.
52.
(A)
(C)
(C)
(B)
(C)
(C)
Competitive Thinking
1.
11.
21.
31.
41.
51.
61.
71.
(D)
(B)
(C)
(B)
(B)
(C)
(C)
(C)
2.
12.
22.
32.
42.
52
62.
72.
(C)
(C)
(B)
(C)
(C)
(D)
(A)
(B)
3.
13.
23.
33.
43.
53.
63.
73.
Hints
Classical Thinking
13.
26.


57.
Critical Thinking
Temperature is a fundamental quantity.
5
2
4
1.
Physical quantity (M)
= Numerical value (n)  Unit (u)
If physical quantity remains constant then
n  1/u  n1u1 = n2u2.
2.
Because in S.I. system, there are seven
fundamental quantities.
2
1 dyne = 10 N, 1 cm = 10 m
103 dyne/cm2 = 103  105/104 N/m2
= 102 N/m2
OR
Using quick conversion for pressure,
1 dyne/cm2 = 0.1 N/m2
103 dyne/cm2 = 103  0.1 = 102 N/m2
3.
=
 d

 100  %
Percentage error = 
 d

 0.01

 100  %
=
 1.03

= 0.97%
mass  pressure m  (F / A) F  V
=
=
density
(m / V)
A
F  (A  s)
= F  s = work
A
6.
 m 
mv = kg 

 sec 
7.
Curie = disintegration/second
21
Std. XI : Triumph Physics
8.

Bxt is unitless.
Unit of B is m1s1.
9.
Y=
10.
Parallactic angle,  = 57
o

 57 
 57 
=  =  
rad
 60  180
 60 
b = Radius of earth = 6.4  106 m
Distance of the moon from the earth,
6.4  106  60  180
b
s=
=
s = 3.86  108 m

57  
11.
12.
13.

15.
16.
17.
21.
23.
24.
22
F L
dyne 10-5 N
.
=
=
= 0.1 N/m2
A DL
cm 2 10-4 m 2
Distance of sun from earth, s = 1.5  1011 m
Angular diameter of sun,

1920 
 1920 

 = 1920 = 
rad
 =
3600 180
 60  60 
Diameter of sun, D = s  
1920 

= 1.5  1011 
3600 180
D  1.4  109 m
 M1L1T 2 
F
= [M1L1T4]
b= 2 =
T 2 
t
25.
F= a x

a=

 M1L1T 2 
F
=  1/ 2  = [M1L1/2T2]
 L 
x
2
bt = F
F
b= 2
t
 M1L1T 2 
=
= [M1L1T4]
2
T 
 M1L1/ 2 T 2 
a
=
= [L1/2 T2]
b
 M1L1T 4 
According to Poiseuille’s formula,
πPr 4
=
8l (dV / dt)


[M1L1T2] = [L2]a [L1T1]b [M1L3]c
= [L2a] [LbTb] [McL3c]
= [Mc L2a + b 3c Tb]
Comparing powers of M, L and T,
c = 1, 2a + b  3c = 1,
b =  2
b=2
2a + 2  3(1) = 1
2a = 2
a=1
[M1L-1T-2 ][L4 ]
[ ] =
= [M1L1T1]
[L1 ][L3 / T1 ]
27.
Let T2 =
Torque = [M1L2T2],
Angular momentum = [M1L2T1]
So mass and length have the same dimensions.
[Dipole moment] = [M0L1T1A1]
[Electric flux]
= [M1L3T3A1]
[Electric field] = [M1L1T3A1]
1 2
Li = energy stored in an inductor
2
= [M1L2T2]
The dimension of a quantity is independent of
changes in its magnitude.
26.



1
= c = velocity of light
00
 M1   L1T 2 
mg
= 1 1  1 1 = [L1T1]
r
 L M T   L 
From F = at + bt2
1 2
M1LT

F
=
= [M1L1T3]
a=
T1 
t
28.
4π 2 a x
G y Mz
42 being pure number is dimensionless.
[M 0 L1T 0 ]x
[M0L0T2] =
[M-1L3T-2 ] y [M1L0 T 0 ]z
 [M0L0T2] = [Lx] [M1L3T2]y [M1]z
Comparing powers of M, L and T
y  z = 0,
x  3y = 0 and 2y = 2
y=1
Substituting value of y,
z = 1, x = 3
4π 2 a 3
Thus, T2 =
GM
T = PaDbSc
[M0L0T1] = [M1L1T2]a [M1L3T0]b [M1L0T2]c
Comparing powers of M, L, T
a + b + c = 0,
 a  3b = 0 and  2a  2c = 1
3
1
and c = 1.
Solving, a = - , b =
2
2
Chapter 01: Measurements
29.
In the given wave equation x denotes
39.
æ xö
displacement. Thus ççç ÷÷÷ has dimensions of T.
è vø
41.

The number of significant figures in all of the
given number is 4.
A vernier calliper has a least count 0.01 cm.
Hence measurement is accurate only upto
three significant figures.
In multiplication or division, final result
should retain the same number of significant
figures as there are in the original number with
the least significant figures.
Area of rectangle = 6  12 = 72 m2
43.
am =
Hence from the principle of homogenity k has
dimensions of T.
30.

42.
a  t2
bx
a = [t2] = [T2]
T2
P=
bx
P=
T 
T2
b=
=
=
Px
 M1L1T 2   L1 
2
 T 4 
 M1 
am = 21.21
a1 = 21.21  20.17= 1.04
a2 = 21.21  21.23 = 0.02
a3 = 0.42
a4 = 0.86
a5 = 0.57
 M1 
a
2 
= [T ] 4 = [M1T2]
b
T 
31.


32.
33.
By principle of dimensional homogeneity
 a 
 V 2  = [P]
 
[a] = [P] [V2] = [M1L1T2]  [L6]
= [M1L5T2]
Dimensions of b are same as that of V,
[b] = [L3]
am =
45.
a
b
 0.005
2nd system
L2 = 1 km
47.
48.
T2 = 1 min
1
 10 5 km   1 /60 min 
n =  L 1   T 1  = 980  
 

 L2  T 2 
46.
s
t2
 1 km   1 min
= 980  105  3600
= 35.28 km min2
 d

 100  %
Percentage error = 
 d


 100  % = 25%
=
 0.020

Let G  cxgypz
Substituting dimensions,
[M1L3T2]= [M0L1T1]x [M0L1T2]y [M1L1T2]z
Comparing powers of M, L, T
 1 = z,
x + y  z = 3 and
 x  2y  2z =  2
Solving, x = 0, y = 2
g = [L1T2]
a = 1, b = 2
1st system
L1 = 1 cm
= 105 km
1
T1 = 1 s = min
60
Δa1 + Δa 2 + Δa 3 + Δa 4 + Δa 5
5
1.04  0.02  0.42  0.86  0.57
=
= 0.58
5
 M1L5T 2 
a 
=  M1L2T 2 
3
 b  =
 L 
Acceleration due to gravity = g =
20.17  21.23  20.79  22.07  21.78
5

2
49.
4
r
 100 = 0.1% and V = r 3
r
3
V
Percentage error in volume =
%
V
3r
= 0.3%
=
r
F
F
P=
= 2
A
l
so maximum error in pressure (P)
F
l
 P

 100 + 2  100
 100  =

F
l
 P
 max
= 4% + 2 × 2% = 8%
 m 2v 

Percentage error in K.E = 
%
v 
 m
= (0.75 + 2  1.85)%
= 4.45%
Maximum possible error in measurement of
L  L
T 
2
=
%
2
T
T 
 L
= (0.1 + 2  3) % = 6.1%
23
Std. XI : Triumph Physics
50.
T = 2π l / g  T2 = 4π2l/g  g =
% error in l =

51.
42 l
T2
1mm
0.1
100 = 0.1%
× 100 =
100
100cm
 0.1

100  = 0.2%
and error in T = 2 
100

% error in g = % error in l + % error in T
= 0.1 + 0.2 = 0.3 %
Energy = force  distance, so if both are increased
by 4 times then energy will increase by 16 times.
13.
1 dyne = 105 N and 1 cm = 102 m
 1 dyne/cm = 103 N/m
108 dyne/cm = 105 N/m

14.
RC is the time constant of RC circuit and
L
  is the time constant of LR circuit. Hence,
R
L
both RC and   have the dimensions of time
R
Alternate method:
coulomb
RC = ohm  farad = ohm 
volt
coulomb coulomb
volt
=

=
volt
ampere
ampere
= second = [T]
L henry
=
Now,
R
ohm
ohm  second
=
ohm
= second = [T]
L
Both RC and
have the dimensions of time.
R
16.
[ 0 L]  [C]
 LV C  V Q

  Current
X 0
t
t
t
V
 l b h 
 100 =  

  100%
V
b
h 
 l
 0.02 0.01 0.02 


=
  100%
 13.12 7.18 4.16 
= 0.77%
I 2 Rt
4.2
H
 I R t 
 %
100 =  2 
% Error,
R
t 
H
 I
= 2  2 + 1 + 1 = 6%
52.
H=
53.
[Energy] = [M1L2T2]
= [M1L1T1] [L1] [T1] = [P1A1/2T1]
54.
Avogadro number (N) represents the number
of atoms in 1 gram mole of an element. i.e., it
has the dimensions of mole1.
55.
12.
As the graph is a straight line , P  Q, or
P
P = Constant  Q i.e.,
= constant.
Q

F=

[G]
24.
W=
Competitive Thinking
3.

4.

24
The van der Waals equation for ‘n’ moles of
the gas is,

n 2a 
 P  2   [V  nb] = nRT
V 

Volume
Pressure
correction
correction
F
 V 2 FlV Fl 4
PV 2 A
 2  2
a= 2 =
n2
n
n
n
Thus, S.I.units of a is N m4/mol2.
From Van der Waal’s equation,
nb has dimensions of volume.
V
b=
n
Thus, S.I. units of b is m3/mol.
Gm1m 2
r2
Fr 2
G=
m1m 2
20.
 M1L1T 2   L2 
= 
= [M1L3T2]
2
 M 
1 2
Kx
2
[W]
[K] = 2
[x ]
 M1L2 T 2 
1 2
= 
 = [M T ]
2
L


25.
Fv
F = kv
 M1L1T 2 
F
k=
=  1 1  = [M1L0T1]
v
 LT 
Chapter 01: Measurements
27.
R=
PV
 M1L1T 2  L3 
1 2 2 1
= 
 = [M L T θ ]

T


28.
F=
x
d

[x] =  F d 
1/ 2
0 1/2
=  M1L1T 2   M1L3T  =  M 3/ 2 L1/ 2 T 2 
29.

30.

31.
X
F=
Linear density
Linear density is mass per unit length
 M1 
[M1L1T2]   1  = [X]
L 
2 0 –2
 [X] = [M L T ]
The van der Waals equation for ‘n’ moles of
the gas is,

n 2a 
P


  [V  nb] = nRT
V2 

Volume
Pressure
correction
correction
F
 V 2 FlV Fl 4
PV 2 A
 2  2
a= 2 =
n
n2
n
n
4
 Fl 
  a    2  = [M1L5T2mol2]
n 
q q
0
= 1 22
4 Fr
[0] =
A2 T2
= [M1 L3 T4 A2]
(M1L1T 2 ) L2
Electric Field =
33.
[0E2] = [0] [E]2
= [M1L3T4A2] [M1L1T3A1]2
= [M1L1T2A0]
OR
1
ε0 E2 = u
2
where u is energy density and has dimensions
[M1L1T2]
Units of solar constant :
W
m2
m2 1
kg
 2  3
3
s
m
s
Dimension  [M1 L0T3]
= kg

37.
c = [T]
v [L1 T 1 ]
=
a=
[T1 ]
t
= [L1T2]
b = v(t + c) = [L1T1]  T1 = [L1]
EJ 2
M 5G 2
=
[M1L2 T 2 ][M1L2 T 1 ]2
[M1 ]5 [M 1L3T 2 ]2
= [M0L0T0]
The dimensions of angle are [M0L0T0].
X
[M 1L2 T 4 A 2 ]
=
3Z2
[M1L0 T 2 A 1 ]2
= [M3L2T8A4]
38.
Y=
39.
Let T  Sxryz
[M0L0T1] = [M1L0T2]x [M0L1T0]y [M1L3T0]z
Comparing powers of M, L, T
x + z = 0,
y  3z = 0 and
 2x = 1
1
3
1
Solving, x = - , y = , z =
2
2
2
Thus, T  S1/2 r3/2 1/2
T = k (r 3ρ / S)1/ 2 = k
40.

[M1L1T 2 ]
Force
=
[A1T1 ]
Charge
[E] = [M1L1T3A1]
32.
35.
36.
ρr 3 / S
In the given equation,
Z
k
should be
dimensionless,
k

Z
[M1L2 T 2 K 1  K1 ]
 [α] =
[L1 ]
= [M1L1T2]

And P =

1 1 2
   [M L T ]
[β] =    1 1 2
 P  [M L T ]
 [β] = [M0L2T0]
41.
V
I
U
[V]  [M1L2T3A1] using V =
q
RA
[]  [M1L3T3A2] using  =
l
1
[]  [M1L3T3A2] using  =

[R]  [M1L2T3A2] using R =
25
Std. XI : Triumph Physics
42.
For vernier scale, where the 10 divisions in
vernier scale matches with 9 division in main
scale and main scale has 10 divisions in 1 cm
1 MSD = 1 mm and 9 MSD = 10 VSD,
Least count = 1 MSD – 1 VSD = 0.1 mm
Hence, correct option is (B).
PV
NT
1
1 2 2
S.I. unit: J K  [M L T K1]
Boltzmann constant (kB) =
Coefficient of viscosity () =
F
 dv 
A 
 dx 
Ns
 [M1 L1 T1]
m2
Water equivalent is the mass of water that will
absorb or lose same quantity of heat as that of
the substance for the same change in
temperature.
S.I. unit : kg  [M1 L0 T0]
Coefficient of thermal conductivity (K)
Q
=
  
At 

 x 
S.I. unit : J/ m s K  [M1 L1 T3 K1]
30 VSD = 29 MSD
29
1 VSD =
MSD
30
L.C. = 1 MSD – 1 VSD
1
 29 
 0.5
= 1   MSD =
30
 30 
= 1 minute
49.
One main scale division, 1 M.S.D. = x cm
One vernier scale division,
(n 1) x
1 V.S.D. =
n
Least count = 1 M.S.D. – 1 V.S.D.
nx nx  x
x
=
=
cm.
n
n
50.
Least count of screw gauge =
51.
30 VSD = 29 MSD
29
MSD
1 VSD =
30
Least count of vernier = 1 M.S.D. – 1 V.S.D.
 29
 0.5
= 0.5    0.5  =
30
 30

Reading of vernier = M.S. reading
+ V.S. reading  L.C.
0.5
= 58.65
= 58.5 + 9 
30
53.
A = 4πr2

Fractional error
S.I. unit :
45.
46.
20 VSD
= 16 MSD
1 VSD
= 0.8 MSD
Least count = MSD – VSD
= 1 mm – 0.8 mm = 0.2 mm
Main scale
0.8 mm
0
0
47.

48.
26
1mm
10
For a given vernier callipers,
1 MSD = 5.15  5.10 = 0.05 cm
2.45
1 VSD =
= 0.049 cm
50
L.C
= 1 MSD  1VSD
= 0.001 cm
Thus, the reading = 5.10 + (0.001  24)
= 5.124 cm
 diameter of cylinder = 5.124 cm
As per the question, the measured value is
3.50 cm. Hence the least count must be
0.01 cm = 0.1 mm
1
mm
100
= 0.01 mm
Diameter = Main scale reading + (Divisions on
circular scale  least count)
1 

= 0 +  52 
 = 0.52 mm
100 

Diameter = 0.052 cm.
A
2r
=
A
r
A
 100 = 2  0.3% = 0.6%
A
4 3
πr
3
Δr
% error in volume = 3 
 100
r
0.1 

= 3×
 100
5.3 

55.
Volume of sphere (V) =
56.
R=
V
R
V I



I
R
V
I
= 3 + 3 = 6%
Chapter 01: Measurements
57.
a 3b2
cd
Given that: P =
 a

= 3   100 
 a

= 3  1% = 3%
 b

error contributed by b = 2   100 
 b

= 2  2% = 4%
 c

error contributed by c =  100  = 3%
 c


d


error contributed by d =  100  = 4%
d


Percentage error in P is given as,
Dp
´100 = (error contributed by a)+(error
p
contributed by b) + (error contributed by c)
+ (error contributed by d)
= 3% + 4% + 3% + 4%
= 14%
61.
error contributed by a

58.
Least count =
  

 = 2% +
  max


= 3.1%

Least count of both instrument
0.5
mm = 5  103mm
d = l =
100
4MLg
Y=
ld 2
l
d
 Y 
=
+2


l
d
 Y  max
l
Error due to l measurement
l
0.5 /100mm
=
= 2%
0.25mm
Error due to d measurement,
0.5
2
d
100 = 0.5 / 100 = 2%
2
=
0.5mm
d
0.25
63.
We have;
l
T = 2
g
Squaring
2 l 
T2 = 4   
g
Pitch
No.of div.in circular scale
0.5
= 0.01 mm
50
Actual reading = 0.01  35 + 3 = 3.35 mm
Taking error into consideration
= 3.35 + 0.03
= 3.38 mm.
60.



0.5
= 0.05 mm
50
Actual measurement
0.5
= 2  0.5 mm + 25 
 0.05 mm
50
= 1 mm + 0.25 mm  0.05 mm
= 1.20 mm
Zero error = 5 
Main Scale Reading (MSR) = 0.5 mm
Circular Scale Division (CSD) = 25th
Number of divisions on circular scale = 50
Pitch of screw = 0.5 mm
0.5
LC of screw gauge =
= 0.01 mm
50
zero error = 5  LC = –0.05 mm
zero correction = +0.05 mm
Observed reading = 0.5 mm + (25  0.01) mm
= 0.75 mm
Corrected reading = 0.75 mm + 0.05 mm
= 0.80 mm
  0.01 

3  2.7  100% 

 

62.
=
59.
0.5
= 0.01 mm
50
Diameter of ball D = 2.5 mm + (20) (0.01)
D = 2.7 mm
M
M
=
=
V 4  D 3
 
3 2
  
M
D
3
 
 =
D
  max M
Least count =

64.

l
T2
Fractional error in g is
g  l
T

2
g
T
l
g = 4
2
g L
 T 
=
+ 2

g
L
 T 
 L
 T  
 2
g = g 

 T 
 L
27
Std. XI : Triumph Physics


Time for 20 oscillations = 40 s
40
Time for 1 oscillation =
20
T=2s
4  2 L 4(3.14) 2  0.98
=
= 9.68 m/s2
g=
T2
 2 2
 0.1
 0.1  
 2

98
 2 


g = 9.68 

 0.1

g = 9.68   0.1
98


65.
Given : T = 2 

L
g

4  2l
g= 2
T
g
 100
% error in g =
g
….(ii)
….(iii)
….(iv)
mv
t
70.
F = ma =

m=

 Ft 
[m] =   = [F1 V1 T1]
v
71.
F
E
E 
[Surface tension] =     2   
(VT) 2 
L L 
Ft
v


–2 –2
72.
[T] = [M1T2]
[] = [M1L1T1]
[] = [M1L3]
From the options given,
T    M1T 2 
= [L1T1] = [v]
   M1L1T 1 
 T 

  100
 T 
EI =
0.1
 0.1 
100  2 
 100 = 1.406%
64
 16 
EII =
0.1
 0.1 
100  2 
 100 = 1.406%
64
 16 

v
EIII =
0.1
 0.1 
100  2 
 100 = 2.72%
20
 9 
73.
Planck constant (h) is related to angular
nh
L
momentum (L) as,
2
 [h] = [L] = [mvr]
Moment of inertia I = mr2
h mvr v
=
= =
I mr 2
r
But  = 2f
h
    [2 f ]  [f ]
I
 M1L2 
ML2
=
= [M1L2T2A2]
2
2
1
1
Q
 A T 
x b
at
From principle of homogeneity, ‘b’ will have
the dimensions of x2
2
28
….(i)
= [E V T ]
These are the dimensions of unit Henry.
69.
[b] = [L2]
Also,
[P] = [M1L2T3]
[t] = [T1]
[L2 ]
[b]
[a] =
=
[P][t] [M1L2T 3 ][T1 ]
[a] = [M1T2]
[L2 ]
[b]
=
= [M1L2T–2]
[a] [M 1T 2 ]

Torsional constant K =

[K] = []
[K] = [M1L2T2]
From (iii) and (iv),
[b]
= [K]
[a]
1
 l 
=    100 + 2
 l 
68.


L
 g = 42. 2
T
% Accuracy in determination of g,
L
T
g
100 + 2
100
100 =
L
T
g
L
t
100  2 100
=
L
t
0.1
1
100  2  100
=
20
90
100 200

= 0.5 + 2.22
=
200 90
= 2.72  3%
66.

Given: P =

T

Chapter 01: Measurements
Evaluation Test
1.
When dimensions of a given physical quantity
are given, the physical quantity is unique.
(A) The statement and its converse both are
true.
(B) The statement and its converse both are
false.
(C) The statement is false but its converse is
true.
(D) The statement is true but its converse is
false.
2.
Two quantities A and B are related by the
A
= m, where m is linear mass
relation
B
density and A is force. The dimensions of B
will be same as that of
(A) latent heat
(B) pressure
(C) work
(D) momentum
3.
The readings of a constant potential difference
are noted four times by a student. The student
averages these readings but does not take into
account the zero error of the voltmeter. The
average measurement of the potential
difference is
Reading 1
Reading 2
Reading 3
Reading 4
(A)
(B)
(C)
(D)
4.
5.
6.
Two full turns of the circular scale of a screw
gauge cover a distance of 1 mm on its main
scale. The total number of divisions on the
circular scale is 50. Further, it is found that the
screw gauge has a zero error of  0.02 mm.
While measuring the diameter of a thin wire, a
student notes the main scale reading of 4 mm
and the number of circular scale divisions in
line with the main scale as 37. The diameter of
the wire is
(A) 4.37 mm
(B) 4.39 mm
(C) 4.74 mm
(D) 4.76 mm
7.
The potential energy U of a particle varies
with distance x from a fixed origin as
A x
where A and B are dimensional
U= 2
x B
constants. The dimensional formula for AB is
(A) [M1L7/2T2]
(B) [M1L11/2T2]
(C) [M1L5/2T2]
(D) [M1L9/2T2]
8.
Assertion: The number 37800 has three
significant digits.
Reason: All non-zero digits are significant.
(A) Assertion is True, Reason is True; Reason
is a correct explanation for Assertion.
(B) Assertion is True, Reason is True; Reason
is not a correct explanation for Assertion.
(C) Assertion is True, Reason is False.
(D) Assertion is False but, Reason is False.
1.176 V
1.178 V
1.177 V
1.176 V
precise and accurate.
precise but not accurate.
accurate but not precise.
not accurate and not precise.
The ‘rad’ is the correct unit used to report the
measurement of
(A) the rate of decay of radioactive source.
(B) the ability of a beam of gamma ray
photons to produce ions in a target.
(C) the energy delivered by radiation to a
target.
(D) the biological effect of radiation.
The dimensions of capacitance in M, L, T and
C (Coulomb) is given as
(A) [M1L2T2C2]
(B) [L2T2C2]
(C) [M1L2T2C2]
(D) [M1L2T2C2]
9.
10.
C
, the dimensions of B and C
DE
are [M0LT1] and [M0LT0], respectively. Find
the dimensions of A, D and E.
(A) A = [M0L0T1], D = [T], E = [LT]
(B) A = [MLT0], D = [T2], E = [T2]
(C) A = [M0LT1], D = [MT], E = [MT]
(D) A = [M0LT1], D = [T], E = [T]
If A = B +
In the measurement of a physical quantity
A2B
X = 1/3 3 . The percentage errors introduced
C D
in the measurements of the quantities A, B, C
and D are 1%, 3%, 4% and 5% respectively.
Then the minimum amount of percentage of
error in the measurement of X is contributed
by
(A) A
(B) B
(C) C
(D) D
29
Std. XI : Triumph Physics
11.
If E = energy, G = gravitational constant,
I = impulse and M = mass, the dimension
GI 2 M
is same as that of
E2
(A) spring constant
(B) wavelength
(C) energy gradient
(D) Rydberg constant
12.
Choose the incorrect statement:
(A) A dimensionally correct equation may
be correct.
(B) A dimensionally correct equation may
be incorrect.
(C) A dimensionally incorrect equation must
be incorrect.
(D) A dimensionally incorrect equation may
be correct.
13.
The radius of a ball is (6.2  0.4) cm. The
percentage error in the volume of the ball is
(A) 11%
(B) 4%
(C) 19%
(D) 9%
14.
The number of particles crossing the unit area
perpendicular to the z-axis per unit time is
 n  n1 
given by N = D  2
 where n1 and n2
 z 2  z1 
are the numbers of particles per unit volume at
z1 and z2 respectively along z-axis. What is the
dimensional formula for the diffusion constant
D?
(A) [M0L1T2]
(B) [M0L2T4]
(C) [M0L1T3]
(D) [M0L2T1]
15.
When a screw gauge is completely closed, zero
of circular scale is 4 divisions above the
reference line of graduation. If L.C. of screw
gauge is 103 cm, the zero error is
(A)  4  103 cm
(B) + 4  103 cm
(C)  0.004 mm
(D) + 0.004 mm
16.
Which of the following is not dimensionless?
(A) Relative refractive index
(B) Relative permittivity
(C) Relative density
(D) Relative velocity
30
17.
The jaws of a vernier callipers touch the inner
wall of calorimeter without any undue
pressure. The position of zero of vernier scale
on the main scale reads 3.48. The 6th of
vernier scale division is coinciding with any
main scale division. Vernier constant of
callipers is 0.01 cm. Find actual internal
diameter of calorimeter, when it is observed
that the vernier scale has a zero error of
– 0.03 cm.
(A) 3.37 cm
(B) 3.57 cm
(C) 3.42 cm
(D) 3.54 cm
18.
The thin metallic strip of vernier callipers
moves downward from top to bottom in such a
way that it just touches the surface of beaker.
Main scale reading of calliper is 6.4 cm
whereas its vernier constant is 0.1 mm. The 4th
of vernier scale division is coinciding with
main scale division. The actual depth of
beaker in mm is (when zero of vernier
coincides with zero of main scale)
(A) 6.64 cm
(B) 6.42 cm
(C) 6.44 cm
(D) 6.13 cm
Answers to Evaluation Test
1.
5.
9.
13.
17.
(C)
(C)
(D)
(C)
(B)
2.
6.
10.
14.
18.
(A)
(B)
(C)
(D)
(C)
3.
7.
11.
15.
(B)
(B)
(B)
(A)
4.
8.
12.
16.
(D)
(B)
(D)
(D)