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) \[M^{-1}L^{-2}T^{-4}A^{-2}\]
Explanation:
10. \[MLT^{-1}\] represents the dimensional formula of
a) Power
b) Momentum
c) Force
d) Couple
Explanation: Momentum = mv = [MLT-1]