## Units and Measurement Questions and Answers Part-18

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 = [ML2T-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 = [ML2T-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

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 $ML^{2}T^{-1}$