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PPM – 1
PHYSICS & MEASUREMENT
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18
Ph. : 9312629035, 8527112111, E-mail [email protected],
www.einsteinclasses.com
PPM – 2
CONCEPTS
UNITS AND DIMENSIONS OF IMPORTANT PHYSICAL QUANTITY
Quantity
SI Unit
Dimensional Formula
1.
Angular Velocity
rad s–1
T–1
2.
Modulus of Elasticity
Nm–2
ML–1T–2
3.
Angular Momentum
kg m2 s–1
ML2T–1
4.
Impulse
Ns
MLT–1
5.
Coefficient of Viscosity
kg m–1 s–1
ML–1T–1
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S.No.
6.
Surface Tension
Nm–1
MT–2
7.
Universal Gravitational
Constant
Nm2kg–2
M–1L3T–2
8.
Specific Heat
J kg–1 K–1
L2T–2–1
9.
Thermal Conductivity
J m–1 s–1 K–1
ML T–3–1
10.
Electric Potential
J C–1 or volt (V)
ML2T–3I–1 (or ML2T–2Q–1)
11.
Electric Resistance
V A–1 or ohm ()
ML2T–3I–2 (or ML2T–1Q–2)
12.
Resistivity
m
ML3T–3I–2 (or ML3T–1Q–2)
13.
Capacitance
CV–1 or farad (F)
M–1 L–2 T4 I2 (or M–1 L–2 T2 Q2)
14.
Inductance
Vs A–1 or henry (H)
ML2T–2I–2 (or ML2Q–2)
15.
Magnetic Induction
NA–1 m–1 or tesla (T)
MT–2I–1(or MT–1Q–1)
16.
Magnetic Flux
Tm2 or weber (Wb)
ML2T–2I–1 (or ML2T–1Q–1)
17.
Permittivity
C2N–1m–2
M–1L–3T4I2 (or M–1L–3T2Q2)
18.
Permeability
Tm A–1 or Wb A–1m–1
MLT–2I–2 (or MLQ–2)
19.
Planck’s Constant
Js
ML2T–1
20.
Boltzmann Constant
JK–1
ML2T–2–1
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18
Ph. : 9312629035, 8527112111, E-mail [email protected],
www.einsteinclasses.com
PPM – 3
EXERCISE
2.
3.
The dimensional formula for the modulus of
rigidity is
(a)
[ML2T–2]
(b)
[ML–1T–3]
(c)
[ML–2T–2]
(d)
[ML–1T–2]
The radio-active decay constant has the same
dimensional formula as
(a)
mole
(b)
frequency
(c)
time
(d)
mass
The dimensions of permittivity (0) of vacuum are
(a)
(c)
4.
–1
3
4 2
M L TI
4 2
Pressure
–3
Consider a new system of units in which c (speed of
light in vacuum), h (Planck’s constant) and G
(gravitational constant) are taken as fundamental
units. Which of the following would correctly
represent mass in this new system ?
(a)
hC
G
(b)
GC
h
(c)
hG
c
(d)
hGC
2 2
(b)
ML T I
(d)
ML3T2I2
(b)
Thrust
12.
(d)
Force
If time T, acceleration A and force F are regarded
as base units, then the dimensional formula of work
is
(a)
Work
(c)
Which of the following pairs has the same
dimensions ?
13.
[FA]
2
[FAT ]
(b)
[FAT]
(d)
[FA2T]
(a)
Impulse and Momentum
Let Q denote the charge on the plates of a
capacitor of capacitance C. The dimensional
formula for Q2/C is
(b)
Specific heat and Latent heat
(a)
[M 2L2T2]
(b)
[ML2T–2]
(c)
Moment of inertia and Moment of
momentum
(c)
[MLT0]
(d)
[M2L2T]
(d)
7.
–3
Energy per unit volume represents
(c)
6.
–1
M LTI
(a)
5.
11.
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1.
14.
Surface tension and tension (force)
What is the SI unit of Stefan-Boltzmann’s constant
?
(a)
W m–2 K–4
(b)
W m2 K4
(c)
W K–4
(d)
erg s–2 K–4
The velocity of a body is given by the equation :
v
b
 ct 2  dt 3
t
A highly rigid cubical block A of small mass M and
side L is fixed rigidly on to another cubical block of
same dimensions and of low modulus of rigidity 
such that the lower face of A completely covers the
upper face of B. The lower face of B is rigidly held
on a horizontal surface. A small force F is applied
perpendicular to one of the side faces of A. After
the forces is withdrawn, block A executes small
oscillations, the time period of which is given by
(a)
2  M L
(c)
2
(b)
2
M
L
(d)
2
M
L
The dimensional formula of b is
(a)
0
(c)
8.
9.
10.
[M 0LT0]
(b)
0
[M L T]
(d)
[ML0T0]
–1
[MLT ]
The dimensional formula of latent heat is
(a)
[M 0L2T–2]
(b)
[MLT2]
(c)
[ML2T–2]
(d)
[MLT–1]
15.
ML

The time depends of physical quantity P is given
2
by P  P0 e  t . The constant  will
The dimensional formula for Rydberg constant is
(a)
be dimensionless
(a)
[M 0LT–1]
(b)
[M 0L–1T0]
(b)
have dimensions T–2
(c)
[M 0L0T0]
(d)
[MLT]
(c)
have dimensions same as that of P
(d)
have dimensions equal to the dimensions
of P multiplied by T–2.
In the equation X = 3YZ2, X ans Z have dimensions
of capacitance and magnetic induction respectively.
In MKSQ system, the dimensional formula of Y is
(a)
(c)
–3
–2
–2
–3
–2
4
–4
[M L T Q ]
8
[M L Q T ]
Einstein Classes,
–2
(b)
[ML ]
(d)
[M –3L–2Q4T4]
16.
µ0 and 0 denote the permeability and permittivity
respectively of free space. The dimensional formula
of µ00 is
(a)
[L–2T2]
(b)
[L–1T]
(c)
[LT–1]
(d)
[L2T–2]
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18
Ph. : 9312629035, 8527112111, E-mail [email protected],
www.einsteinclasses.com
PPM – 4
17.
The number of particles given by
n  D
25.
n 2  n1
x 2  x1
are crossing a unit area perpendicular to x-axis in
unit time, where n 1 and n 2 are the number of
particles per unit volume for the values x1 and x2 of
x respectively. Then the dimensional formula of
diffusion constant D is
8%
[M 0LT–3]
(d)
[M 0L2T–1]
(a)
5%
(b)
1%
(c)
8%
(d)
10%
[M 0L0T0A0]
(b)
[M –1L3T2A]
[ML3T–4A–2]
(d)
[M –1L–3T4]
The frequency of vibration f of a mass m suspended
from a spring of spring constant k is given by
relation of the type f = cm xk y , where c is a
dimensionless constant. The values of x and y are
27.
1/2, 1/2
(b)
–1/2, –1/2
1/2, –1/2
(d)
–1/2, 1/2
28.
If E, m, J and G represent energy, mass, angular
momentum and gravitational constant respectively,
then the dimensional formula of EJ2/m5G2 is
(c)
angle
(b)
length
mass
(d)
time
If gravitational constant G, velocity of light c and
Planck’s constant h are taken as the fundamental
quantities, then the dimensional formula for length
is
(a)
(c)
[G–1/2c–3/2h1/2]
(b)
[G1/2c–3/2h1/2]
[G–1/2c3/2h–1/2]
(d)
[G1/2c–3/2h–1/2]
29.
30.
(c)
1
 0 E 2 (0 = permitivity of free
2
space and E = electric field) are
The dimensions of
MLT–2I2
(b)
MLT–2I–2
ML–1T–2I2
(d)
ML–1T–2I–2
If E and B respectively represents electric field and
displacement
(b)
velocity
(c)
acceleration
(d)
angle
If h and e respectively represents Planck’s constant
h
and electronic charge, then the dimensions of  
e
are the same as those of
(a)
magnetic field
(b)
electric field
(c)
magnetic flux
(d)
electric flux
Einstein Classes,
MLT–1
(b)
ML2T–2
(c)
ML–1T–2
(d)
ML2T–1
V
where 0 is the
t
permitivity of free space, L is a length, V is a
potential difference and t is a time interval. The
dimensional formula for X is the same as that of
A quantity X is given by  0 L
(a)
resistance
(b)
charge
(c)
voltage
(d)
current
The dimensional equation for magnetic flux is
(a)
ML2T–2I–1
(b)
ML2T–2I–2
(c)
ML–2T–2I–1
(d)
ML–2T–2I–2
In the measurement of a physical quantity
A 2B
. The percentage errors introduced in
C1 / 3 D 3
the measurements of the quantities A, B, C and D
are 2%, 2%, 4% and 5% respectively. Then the
minimum amount of percentage of error in the
measurement of X is contributed by
31.
E
magnetic induction field, then the ratio
has the
B
dimensions of
(a)
(a)
X
What are the dimensions of permeability (µ0) of
vacuum ?
(a)
24.
(d)
(c)
(a)
23.
5%
[M 0L2T–1]
(c)
22.
(c)
(b)
(a)
21.
3%
[M 0LT2]
(c)
20.
(b)
(a)
(a)
19.
1%
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18.
(a)
The percentage errors in the measurements of the
length of a simple pendulum and its time period
are 2% and 3% respectively. The maximum error
in the value of the acceleration due to gravity
obtained from these measurements is
1 e2
The dimensional formula of
is
 0 hc
26.
The error in the measurement of the radius of a
sphere is 1%. The error in the measurement of the
volume is
32.
(a)
A
(b)
B
(c)
C
(d)
D
If the value of resistance is 10.845 ohm and the value
of current is 3.23 ampere, the potential is 35.02935
volt. Its value in significant number would be
(a)
3.55 volt
(b)
35.0 volt
(c)
35.029 volt
(d)
35.030 volt
The volume of a sphere is 1.76 m3. The volume of
25 such spheres taking into account the significant
figures is
(a)
0.44 × 102 m2
(b)
44.0 m3
(c)
44 m3
(d)
44.00 m3
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18
Ph. : 9312629035, 8527112111, E-mail [email protected],
www.einsteinclasses.com
PPM – 5
34.
35.
How many wavelengths of Kr86 are there in one
metre
(a)
1553164.13
(b)
1650763.73
(c)
2348123.73
(d)
652189.63
The dimensions of coefficient of viscosity are
(a)
ML–1T–1
(b)
MT–1
(c)
MLT–2
(d)
ML–3
In C.G.S. system the magnitude of the force is 100
dynes. In another system where the fundamental
physical quantities are kilogram, meter and minute,
the magnitude of the force is
(a)
0.036
(b)
0.36
(c)
3.6
(d)
36
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33.
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Einstein Classes,
d
b
a
a
a
a
a
a
b
d
a
c
b
d
b
a
d
a
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
d
a
d
b
b
c
b
c
c
d
a
c
b
b
b
a
c
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18
Ph. : 9312629035, 8527112111, E-mail [email protected],
www.einsteinclasses.com
PPM – 6
TEST YOURSELF
8.
1.
v2
With the usual notations, the equation tan  
said
rg
List 1
to give the angle of banking  is
A.
Henry-amp/
sec
numerically correct only
II.
Watt
B.
Farad-volt
(c)
both numerically and dimensionally
correct
III.
Volt
C.
Coulomb-volt
IV.
Coulomb
D.
Oersted-cm
(d)
neither numerically nor dimensionally
correct
E.
Amp-gauss
F.
Amp2-ohm
(b)
Which of the following does not have the
dimensions of frequency ?
(c)
1
CR
(b)
1
(d)
LC
(c)
(a)
I-A, II-F, III-E, IV-D
R
L
(b)
I-C, II-F, III-A, IV-B
(c)
I-C, II-F, III-A, IV-E
C
L
(d)
I-B, II-F, III-A, IV-C
9.
N m2
(b)
N m4
N m–3
(d)
N m–2
The dimensional formula of [ML–1T–2] does not
represents the following
(a)
(b)
(c)
(d)
5.
Codes :
a 

In the equation  P 
 (V – b) = RT, the SI unit
V2 

of a is
(a)
4.
List 2
Joule
dimensionally correct only
(a)
3.
answer
I.
(a)
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2.
Match list 1 with list 2 and select the correct
using the codes given below the lists.
stress
10.
While measuring acceleration due to gravity by a
simple pendulum, a positive error of 2%, is made
in the length of the pendulum and a negative error
of 2% is made in the value of time period. The
percentage error in the measurement of g is
(a)
6%
(b)
8%
(c)
10%
(d)
12%
The specific resistance  of a circular wire of
radius r, resistance R and length l is given by

power
r 2 R
l
Given : r = 0.24 ± 0.02 cm, R = 30 ± 1  and l = 4.80
± 0.01 cm. The percentage error in  is nearly
pressure
Young’s modulus
What is the dimensional formula of
(a)
7%
(b)
9%
(c)
13%
(d)
20%
Planck ' s cons tan t
?
Linear momentum
(a)
(c)
6.
(b)
[M0L0T]
[M 0LT0]
(d)
[MLT–1]
Coefficient of thermal conductivity has the
dimensions
(a)
(c)
7.
[M 0L0T0]
[MLT–3K–1]
3
–3
–2
[ML T K ]
(b)
(d)
[ML3T3K2]
2
3
–3
ANSWERS
2
[M L T K ]
One second is defined to be equal to
1.
c
6.
a
(a)
1650763.73 periods of krypton clock
2.
d
7.
d
(b)
652189.63 periods of krypton clock
3.
b
8.
b
(c)
1650763.73 periods of cesium clock
(d)
9192631770 periods of cesium clock
4.
b
9.
a
5.
c
10.
d
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18
Ph. : 9312629035, 8527112111, E-mail [email protected],
www.einsteinclasses.com