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 $=\left[MLT^{- 2}\right]$
From the relation given in the problem $\Rightarrow \left[B\right]=\frac{\left[A\right]}{\left[m\right]}=\frac{\left[MLT^{- 2}\right]}{\left[ML^{- 1}\right]}=\left[L^{2} T^{- 2}\right]$

Here
Pressure $=\frac{f o r c e}{a r e a}=\left[\right.ML^{- 1}T^{- 2}\left]\right.$
Work
$=Force.displacement=\left[\right.ML^{2}T^{- 2}\left]\right.$
Latent heat $=\frac{H e a t}{m a s s}=\left[\right.L^{2}T^{- 2}\left]\right.$
This is same dimension as that of given in question.