PHYS 101 Previous Exam Problems –
CHAPTER
Measurement
1
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)
Dr. M. F. Al-Kuhaili – PHYS 101 – Chapter 1 Page 1
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)
Dr. M. F. Al-Kuhaili – PHYS 101 – Chapter 1 Page 2
