Question

A relation $m=\frac{A}{B}$ is given where $m$ is the linear mass density and $A$ and $B$ are some other physical quantities. If it is given that $A$ is force, then quantity $B$ has dimensions of which physical quantity given in the options?

• A. Pressure
• B. Work
• C. Latent heat
• D. None of the above

Answer 1

Answer: (C)

$m=$ linear mass density $=$ mass per unit length $=\left[\frac{M}{L}\right]$
$A=$ force $=\left[ML{T}^{-2}\right]$
From the relation given in the problem $\Rightarrow \left[B\right]=\frac{\left[A\right]}{\left[m\right]}=\frac{\left[ML{T}^{-2}\right]}{\left[M{L}^{-1}\right]}=\left[L^2{T}^{-2}\right]$

Here
Pressure $=\frac{force}{area}=[M{L}^{-1}{T}^{-2}]$
Work
$=Force.displacement=[M{L}^2{T}^{-2}]$
Latent heat $=\frac{Heat}{mass}=[L^2{T}^{-2}]$
This is same dimension as that of given in question.