Question

E, m,l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{E{l}^2}{m^2{G}^2}$ are

• A. $\left[M^0{L}^0{T}^0\right]$
• B. $\left[M^0{L}^0{T}^1\right]$
• C. $\left[M^0{L}^1{T}^1\right]$
• D. $\left[M^0{L}^1{T}^{-1}\right]$

Answer 1

The correct option is A $\left[M^0{L}^0{T}^0\right]$

[E] = $\left[M{L}^2{T}^{-2}\right]$, [m]=[M], [l] = $\left[M{L}^2{T}^{-1}\right]$ and $\left[G\right]=\left[M^{-1}{L}^3{T}^{-2}\right]$ Substituting the dimension of above quantities in the given formula :

$\frac{E{l}^2}{m^2{G}^2}=\frac{\left[M{L}^2{T}^{-2}\right][M{L}^2{T}^{-1}{]}^2}{\left[M^5\right][M^{-1}{L}^3{T}^{-2}{]}^2}=\frac{M^3{L}^6{T}^{-4}}{M^3{L}^6{T}^{-4}}=\left[M^0{L}^0{T}^0\right]$