First slide

Dimensions of physical quantities

Question

The quantities A and B are related by the relation A/B = m, where m is the linear mass density and A is the force, the dimensions of B will be

Moderate

A

Same as that of pressure
B

Same as that of work
C

That of momentum
D

Same as that of latent heat

Solution

$\begin{array}{l} \frac{A}{B} = m, B = \frac{A}{m} = \frac{Force}{Linear density} = \frac{M L T^{- 2}}{M L^{- 1}} \\ ∴ B = [M^{0} L^{2} T^{- 2}] \\ Latent heat = \frac{Heat energy}{Mass} = \frac{M L^{2} T^{- 2}}{M} = [M^{0} L^{2} T^{- 2}] \end{array}$
Thus, B has same dimensions as that of latent heat.

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