Physics - Unit & Dimension Question with Solution | TestHub

From the table: $[X]=[T],[Y]=[L{T}^{-1}]$

$[Z]=[M{L}^2{T}^{-1}]$

$[W]=[ML{T}^{-2}]$

$\left[\frac{Z}{WY}\right]=\frac{[M{L}^2{T}^{-1}]}{[ML{T}^{-2}][L{T}^{-1}]}=[T^2]$

So $\sqrt{\frac{Z}{WY}}$ has the dimension of X. Both (A) and (D) are possible ($2\pi$ is a pure number).

$\left[\frac{X^{2}YW}{Z}\right]=[M^0{L}^0{T}^0]$, so $\tan \left(\frac{X^{2}YW}{Z}\right)$ is allowed. (B) is possible.

$\left[\frac{Z}{YW{X}^2}\right]=[M^0{L}^0{T}^0]$, so $\exp \left(-\frac{Z}{YW{X}^2}\right)$ is allowed. (C) is possible.