## Units and Measurement Questions and Answers Part-14

1. The quantities A and B are related by the relation, $m=A\diagup B$  , where m is the linear density and A is the force. The dimensions of B are of
a) Pressure
b) Work
c) Latent heat
d) None of the above

Explanation: m = linear density = mass per unit length = $\left[\frac{M}{L}\right]$
A= force = [MLT-2]
$[B]=\frac{[A]}{[m]}=\frac{[MLT^{-2}]}{[ML^{-1}]}=[L^{2}T^{-2}]$

2. The velocity of water waves v may depend upon their wavelength $\lambda$, the density of water $\rho$ and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as
a) $V^{2}\propto\lambda g^{-1}\rho^{-1}$
b) $V^{2}\propto g\lambda \rho$
c) $V^{2}\propto g\lambda$
d) $V^{2}\propto g^{-1}\lambda^{-3}$

Explanation:

3. The dimensions of Farad are
a) $M^{-1}L^{-2}T^{2}Q^{2}$
b) $M^{-1}L^{-2}TQ$
c) $M^{-1}L^{-2}T^{-2}Q$
d) $M^{-1}L^{-2}TQ^{2}$

Explanation:

4. The dimensions of resistivity in terms of M,L,T and Q where Q stands for the dimensions of charge, is
a) $ML^{3}T^{-1}Q^{-2}$
b) $ML^{3}T^{-2}Q^{-1}$
c) $ML^{2}T^{-1}Q^{-1}$
d) $MLT^{-1}Q^{-1}$

Explanation: $\rho = \frac{RA}{l}$  i.e. dimension of resistivity is [ML3T-1Q-2]

5. The equation of a wave is given by $Y=A\sin\omega\left(\frac{x}{v}-k\right)$    where $\omega$ is the angular velocity and v is the linear velocity. The dimension of k is
a) LT
b) T
c) $T^{-1}$
d) $T^{2}$

Explanation:

6. The dimensions of coefficient of thermal conductivity is
a) $ML^{2}T^{-2}K^{-1}$
b) $MLT^{-3}K^{-1}$
c) $MLT^{-2}K^{-1}$
d) $MLT^{-3}K$

Explanation:

7. Dimensional formula of stress is
a) $M^{0}LT^{-2}$
b) $M^{0}L^{-2}T^{-2}$
c) $ML^{-1}T^{-2}$
d) $ML^{2}T^{-2}$

Explanation:

8. Dimensional formula of velocity of sound is
a) $M^{0}LT^{-2}$
b) $LT^{0}$
c) $M^{0}LT^{-1}$
d) $M^{0}L^{-1}T^{-1}$

Explanation: $M^{0}LT^{-1}$

9. Dimensional formula of capacitance is
a) $M^{-1}L^{-2}T^{4}A^{2}$
b) $ML^{-2}T^{4}A^{-2}$
c) $MLT^{-4}A^{-2}$
d) $M^{-1}L^{-2}T^{-4}A^{-2}$

10. $MLT^{-1}$ represents the dimensional formula of