1. The dimension of quantity \[\left(L\diagup RCV\right)\] is

a) \[\left[A\right]\]

b) \[\left[A^{2}\right]\]

c) \[\left[A^{-1}\right]\]

d) None of these

Explanation:

2. The dimension of the ratio of angular to linear momentum is

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

b) \[M^{1}L^{1}T^{-1}\]

c) \[M^{1}L^{2}T^{-1}\]

d) \[M^{-1}L^{-1}T^{-1}\]

Explanation:

3. The pair having the same dimensions is

a) Angular momentum, work

b) Work, torque

c) Potential energy, linear momentum

d) Kinetic energy, velocity

Explanation: Dimension of work and torque = [ML

^{2}T

^{-2}]

4. The dimensions of surface tension are

a) \[ML^{-1}T^{-2}\]

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

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

d) \[MT^{-2}\]

Explanation:

5. In the following list, the only pair which have different dimensions, is

a) Linear momentum and moment of a force

b) Planck's constant and angular momentum

c) Pressure and modulus of elasticity

d) Torque and potential energy

Explanation: Linear momentum = Mass * Velocity =[MLT

^{-1}]

Moment of a force = Force * Distance = [ML

^{2}T

^{-2}]

6. If R and L represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency:

a) \[\frac{R}{L}\]

b)\[\frac{L}{R}\]

c) \[\sqrt{\frac{R}{L}}\]

d) \[\sqrt{\frac{L}{R}}\]

Explanation:

7. If velocity v , acceleration A and force F are chosen as fundamental quantities, then the dimensional formula of angular momentum in
terms of v, A and F would be

a) \[FA^{-1}v\]

b) \[Fv^{3}A^{-2}\]

c) \[Fv^{2}A^{-1}\]

d) \[F^{2}v^{2}A^{-1}\]

Explanation:

8. The dimensions of permittivity \[\epsilon_{0}\] are

a) \[A^{2}T^{2}M^{-1}L^{-3}\]

b) \[A^{2}T^{4}M^{-1}L^{-3}\]

c) \[A^{-2}T^{-4}ML^{3}\]

d) \[A^{2}T^{-4}M^{-1}L^{-3}\]

Explanation:

9. Dimensions of the following three quantities are
the same

a) Work, energy, force

b) Velocity, momentum, impulse

c) Potential energy, kinetic energy, momentum

d) Pressure, stress, coefficient of elasticity

Explanation: [Pressure] = [Stress] = [coefficient of elasticity] = [ML

^{-1}T

^{-2}]

10. The dimensions of Planck's constant and angular momentum are respectively

a) \[ML^{2}T^{-1}\] and \[MLT^{-1} \]

b) \[ML^{2}T^{-1}\] and \[ML^{2}T^{-1} \]

c) \[MLT^{-1}\] and \[ML^{2}T^{-1} \]

d) \[MLT^{-1}\] and \[ML^{2}T^{-2} \]

Explanation: \[ML^{2}T^{-1}\] and \[ML^{2}T^{-1} \]