Physics - Unit & Dimension Question with Solution | TestHub

To find the dimensions of the given expression, we first list the dimensions of each quantity:

Energy (E): $[M{L}^2{T}^{-2}]$

Mass (m): $[M]$

Angular Momentum (L): $[M{L}^2{T}^{-1}]$

Gravitational Constant (G): $[M^{-1}{L}^3{T}^{-2}]$

Now substitute these into the expression:

$$\frac{E{L}^2}{m^5{G}^2}=\frac{[M{L}^2{T}^{-2}][M{L}^2{T}^{-1}{]}^2}{[M{]}^5[M^{-1}{L}^3{T}^{-2}{]}^2}$$

$$=\frac{[M{L}^2{T}^{-2}][M^2{L}^4{T}^{-2}]}{[M^5][M^{-2}{L}^6{T}^{-4}]}=\frac{[M^3{L}^6{T}^{-4}]}{[M^3{L}^6{T}^{-4}]}=[M^0{L}^0{T}^0]$$

The expression is dimensionless, which corresponds to "angle" as angles are dimensionless.

The final answer is $\boxed{A}$