A relation $\mathrm{m}=\frac{\mathrm{A}}{\mathrm{B}}$ 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?

m = linear mass density = ass

per unit length $=\left[\frac{\mathrm{M}}{\mathrm{L}}\right]$

$\mathrm{A}=\text{ force }=\left[{\mathrm{MLT}}^{-2}\right]$

From the relation given in the problem

$\Rightarrow \left[\mathrm{B}\right]=\frac{\left[\mathrm{A}\right]}{\left[\mathrm{m}\right]}=\frac{\left[{\mathrm{MLT}}^{-1}\right]}{\left[{\mathrm{ML}}^{-1}\right]}=\left[{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

Here

$\text{ Pressure }=\frac{\text{ force }}{\text{ area }}=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$

Work

= Force. displacement

$=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$

$\text{ Latent heat }=\frac{\text{ Heat }}{\text{ mass }}=\left[{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

This is same dimension as that of given in question.