PHYS 101 Previous Exam Problems
CHAPTER
1
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Measurement
Units conversion
Dimensional analysis
Density
1. The position y of a particle moving along the y axis depends on the time t according to the equation
=
y At − Bt 2 . What are the dimensions of the quantities A and B, respectively? (Ans: L/T, L/T2)
2. The position x of a particle is given by: x = Bt2 + (C/B)t, where x is in meters and t is in seconds. What is
the dimension of C? (Ans: L2/T3)
3. Suppose A = Bn/C m, where A has dimensions [LT], B has dimensions [L2T–1], and C has dimensions [LT2].
What are the values of the exponents n and m? (Ans: n = 1/5 ; m = −3/5)
4. One shake = 10-8 seconds. Find out how many nano seconds (ns) are there in 1 shake. (1 nano = 10-9)
(Ans: 10 ns )
5. Express the speed of sound, which is equal to 330 m/s, in miles/h. (1 mile = 1609 m) (Ans: 738 miles/h)
6. Using the fact that the speed of light in space is about 3.00×108 m/s, determine how many miles will light
travel in one hour. (1 mile = 1.61 km) (Ans: 6.71× 108 miles)
7. A student remembers that it takes roughly 8.4 minutes for the sun's light to reach the Earth. Using this
information and the fact that the speed of light is (3.0 × 108) m/s, estimate the distance to the sun in km.
(Ans: 1.50×108 km)
8. An empty fuel tank of a car needs 50 liters of gasoline to fill up. Find the volume of the fuel tank in m3.
(1 milliliter = 1 cm3) (Ans: 0.050)
9. A swimming pool is filled with 16500 ft3 of water. What is the volume of water in m3?
(12 inch = 1 ft, and 2.54 cm = 1 inch) (Ans: 467 m3)
10. The mass of 1.0 cm3 of gold is 19.3 g. What is the mass of a solid cube of gold having a side of 0.70 cm?
(Ans: 6.6 × 10–3 kg)
11. A cube of copper has a mass of m = 126 g. Find the number of copper atoms in this cube. Atomic mass of
copper = 63.0 g/mole; Avogadro number = 6.02×1023 atoms/mole. (Ans: 1.20 × 1024)
12. From the fact that the average density of the Earth is 5.50 g/cm3 and its mean radius is 6.37×106 m,
calculate the mass of the Earth? (Ans: 5.95 × 1024 kg)
13. What is the mass of an aluminum cylinder of density 2.70 g/cm3, radius 2.30 cm, and a height of 1.40 m?
(Ans: 6.28 kg)
14. What is the density of a nucleus of volume 3.4×103 fm3 and mass of 100 u? (1 fm = 10-15 m, 1 u = 1.7 ×
10-27 kg) (Ans: 5.0 × 1016 kg/m3)
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Dr. M. F. Al-Kuhaili – PHYS 101 – Chapter 1
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15. The average radius of a nucleus is R = 10.0 fm. Find the density of the nucleus which has a mass of 15u.
(1 fm = 10-15 m, 1 u = 1.66 × 10-27 kg) (Ans: 5.94×1015 kg/m3)
16. A drop of oil (mass = 0.90 milligram, and density = 918 kg/m3) spreads out on a surface and forms a
circular thin film of radius = 41.8 cm and thickness h. Find h in nano meter (nm). (Ans: 1.8 nm)
17. How many molecules of water are there in a cup containing 250 cm3 of water? Molecular mass of water =
18 g/mole; density of water = 1.0 g/cm3; Avogadro’s number = 6.02×1023 molecules/mole. (Ans: 8.4 × 1024)
18. The speed of sound v in a fluid depends upon the fluid density ρ and its bulk modulus B as follows:
v = ρn.Bm. Using dimensional analysis, find the values of constants n and m, respectively. The unit of density ρ
is kg/m3 and that of bulk modulus B is kg/(m.s2). (Ans: -1/2, +1/2)
19. Consider the following physical relation: M = C ρa.rb, where M is mass, ρ is density, r is distance, and a
and b are exponents. C is a dimensionless constant. What are the values of a and b so that the equation is
dimensionally correct? (Ans: a = 1 and b = 3)
20. The force F applied on a particle is given by the relation F = K ρ A B2, where K is a dimensionless
constant, ρ is a density and A is an area. Find the dimension of B. (Ans: L/T)
21. The average density of blood is 1.06×103 kg/m3. If you donate one pint of blood, what is the mass of the
blood you have donated, in grams? [1 pint = 1/2 Liter, 1 Liter = 1000 cm3] (Ans: 530)
22. The mass of a piece of card board is 20 g. Its length and width are 8.0 and 3.0 inches, respectively. If the
thickness of the card board is 0.50 mm, what is the density of the card board in kg/m3? [1 inch = 2.54 cm]
(Ans: 2.58 × 103)
23. A light-year is the distance traveled by light in one year (365 days). Express a light-year in kilometers if
the speed of light is 3.0×108 m/s. (Ans: 9.5×1012 km)
24. A 0.19-kg solid sphere has a radius of 21 mm. What is its density? (Ans: 4.9×103 kg/m3)
25. The density of iron is 7.86 g/cm3, and the mass of an iron atom is 9.30 × 10-23 g. How many iron atoms are
there in 1.00 in3 of iron? [1 in = 2.54 cm] (Ans: 1.39 × 1024 atoms)
Dr. M. F. Al-Kuhaili – PHYS 101 – Chapter 1
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A B C D E
Conceptual Problems
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1. Which formula could be correct for the speed v of ocean waves in terms of the density ρ of sea water, the
acceleration of free fall g, the depth h in the ocean, and the wave length λ?
(Note: Unit for wave length λ is meter (m) and unit for density ρ is kg/m3)
2. Suppose the speed of a wave on a string is given by v = K τm µn, where K is a dimensionless constant, τ is the
tension in the string, and µ is the mass per unit length of the string. Find the values of m and n.
A)
m = +1/2, n = −1/2
B)
m = +1/2, n = +1/2
C)
m = −1/2, n = −1/2
D)
E)
m = +3/2, n = −3/2
m = +1/2, n = −3/2
3. Work is defined as the scalar product of force and displacement. Power is defined as the rate of change of
work with time. The dimension of power is
A.
M L2 T-3
B.
M L2 T-2
C.
M L3 T-2
D.
M L2 T-1
E.
M L T-2
4. Pressure, P, is a physical quantity defined as: P = F/A, where F is force, and A is the area of the surface on
which F is applied. Find the dimensions of P.
A. M/(LT2)
B. ML/T2
C. MT2/L
D. ML/T
E. L/T2
Dr. M. F. Al-Kuhaili – PHYS 101 – Chapter 1
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