Physics - Unit & Dimension Question with Solution | TestHub

(A) $[\mathrm{k}]=\frac{\mathrm{PV}}{\mathrm{NT}}=\frac{{\mathrm{ML}}^2{\mathrm{T}}^{-2}}{\mathrm{K}}={\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}$
(B) $[\eta ]=\frac{\mathrm{F}}{6\pi \mathrm{rv}}=\frac{{\mathrm{MLT}}^{-2}}{{\mathrm{L}}^2{\mathrm{T}}^{-1}}={\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}$
(C) $[\mathrm{h}]=\frac{\mathrm{E}}{\mathrm{f}}=\frac{{\mathrm{ML}}^2{\mathrm{T}}^{-2}}{{\mathrm{T}}^{-1}}={\mathrm{ML}}^2{\mathrm{T}}^{-1}$
(D) $\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{k}\frac{\mathrm{AdT}}{\mathrm{dx}}$
$\mathrm{k}=\frac{\left({\mathrm{ML}}^2{\mathrm{T}}^{-3}\right)\mathrm{L}}{{\mathrm{L}}^2\cdot \mathrm{K}}={\mathrm{MLT}}^{-3}{\mathrm{K}}^{-1}$