Unit – 1 Physics : Multiple Choice Answers

1. One of the combinations from the fundamental physical constants is $\frac{hc}{G}$. The unit of this expression is

a) kg$^2$
b) m$^3$
c) s$^{-1}$
d) m
Answer: a) kg$^2$

2. If the error in the measurement of radius is 2%, then the error in determination of volume of the sphere will be

a) 8%
b) 2%
c) 4%
d) 6%
Answer: d) 6%

3. If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively, then the error in measurement of acceleration due to gravity is

a) 4%
b) 5%
c) 6%
d) 7%
Answer: d) 7%

4. The length of a body is measured as 3.51 m. If the accuracy is 0.01 m, then the percentage error in the measurement is

a) 351%
b) 1%
c) 0.28%
d) 0.035%
Answer: c) 0.28%

5. Which of the following has the highest number of significant figures?

a) $0.007\,m^2$
b) $2.64 \times 10^{24}\,kg$
c) $0.0006032\,m^2$
d) $6.3200\,J$
Answer: d) $6.3200\,J$

6. If $\pi = 3.14$, then the value of $\pi^2$ is

a) 9.8596
b) 9.860
c) 9.86
d) 9.9
Answer: c) 9.86

7. Round off the following number 19.95 into three significant figures

a) 19.9
b) 20.0
c) 20.1
d) 19.5
Answer: b) 20.0

8. Which of the following pairs of physical quantities have the same dimension?

a) force and power
b) torque and energy
c) torque and power
d) force and torque
Answer: b) torque and energy

9. The dimensional formula of Planck’s constant $h$ is

a) $[ML^2T^{-1}]$
b) $[ML^2T^{-3}]$
c) $[MLT^{-1}]$
d) $[ML^3T^{-3}]$
Answer: a) $[ML^2T^{-1}]$

10. The velocity of a particle is given by $v = at + bt^2$. The dimensions of $b$ is

a) $[L]$
b) $[LT^{-1}]$
c) $[LT^{-2}]$
d) $[LT^{-3}]$
Answer: b) $[LT^{-1}]$

11. The dimensional formula for gravitational constant $G$ is

a) $[ML^3T^{-2}]$
b) $[M^{-1}L^3T^{-2}]$
c) $[M^{-1}L^2T^{-2}]$
d) $[ML^3T^2]$
Answer: b) $[M^{-1}L^3T^{-2}]$

12. The density of a material in CGS system is $4\,g\,cm^{-3}$. If the unit of length is 10 cm and unit of mass is 100 g, the density is

a) 0.04
b) 0.4
c) 40
d) 400
Answer: c) 40

13. If force is proportional to square of velocity, the dimension of proportionality constant is

a) $[MLT^0]$
b) $[MLT^{-1}]$
c) $[ML^{-2}T]$
d) $[ML^{-1}T^0]$
Answer: d) $[ML^{-1}T^0]$

14. The dimension of $(\mu_0\epsilon_0)^{-1/2}$ is

a) length
b) time
c) velocity
d) force
Answer: c) velocity

15. Which of the following combinations has the dimension of length?

a) $\dfrac{\sqrt{hG}}{c^2}$
b) $\dfrac{\sqrt{hG}}{c^5}$
c) $\sqrt{\dfrac{hc}{G}}$
d) $\sqrt{\dfrac{Gc}{h^2}}$
Answer: a) $\dfrac{\sqrt{hG}}{c^2}$