1. Let \[\left(\epsilon_{0}\right)\] denotes the dimensional formula of the permittivity of the vacuum and \[\left(\mu_{0}\right)\] that of the
permeability of the vacuum. If M = mass, L = lenth, T = time and l = electric current, then

a) \[\left[\epsilon_{0}\right]=M^{-1}L^{-3}T^{2}I\]

b) \[\left[\epsilon_{0}\right]=M^{-1}L^{-3}T^{4}I^{2}\]

c) \[\left[\mu_{0}\right]=MLT^{-2}I^{-2}\]

d) Both b and c

Explanation: Both b and c

2. Dimensions of CR are those of

a) Frequency

b) Energy

c) Time period

d) Current

Explanation:

3. The physical quantity that has no dimensions

a) Angular Velocity

b) Linear momentum

c) Angular momentum

d) Strain

Explanation: Strain has no dimensions

4. \[ML^{-1}T^{-2}\] represents

a) Stress

b) Young's Modulus

c) Pressure

d) All the above three quantities

Explanation: All the above three quantities

5. Dimensions of magnetic field intensity is

a) \[M^{0}L^{-1}T^{0}A^{1}\]

b) \[MLT^{-1}A^{-1}\]

c) \[ML^{0}T^{-2}A^{-1}\]

d) \[MLT^{-2}A\]

Explanation:

6. The force F on a sphere of radius \['a'\] moving in a medium with velocity 'v' is given by \[F=6\pi\eta av\] . The dimensions of \[\eta\] are

a) \[ML^{-1}T^{-1}\]

b) \[MT^{-1}\]

c) \[MLT^{-2}\]

d) \[ML^{-3}\]

Explanation:

7. Which physical quantities have the same dimension

a) Couple of force and work

b) Force and power

c) Latent heat and specific heat

d) Work and power

Explanation:

8. Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful

a) \[A\diagup B\]

b) \[A+ B\]

c) \[A- B\]

d) None

Explanation: Quantities having different dimensions can only be divided or multiplied but they cannot be added or subtracted.

9. The physical quantity which has the dimensional formula \[M^{1}T^{-3}\] is

a) Surface tension

b) Solar constant

c) Density

d) Compressibility

Explanation:

10. A force F is given by \[F=at+bt^{2}\] where t is time. What are the dimensions of a and b

a) \[MLT^{-3}\] and \[ML^{2}T^{-4}\]

b) \[MLT^{-3}\] and \[MLT^{-4}\]

c) \[MLT^{-1}\] and \[MLT^{0}\]

d) \[MLT^{-4}\] and \[MLT^{1}\]

Explanation: From the principle of dimensional homogenity