Question

If $E,M,J$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively, then $\frac{E{J}^2}{M^5{G}^2}$ has the dimensions of

• A. Length
• B. Mass
• C. Time
• D. Angle

Answer 1

The correct option is D Angle

Given,

Energy, $\left[E\right]=\left[M^1{L}^2{T}^{-2}\right]$

$\left[mass\right]=\left[M^1\right]$

Angular momentum, $\left[J\right]=\left[M^1{L}^2{T}^{-1}\right]$

Gravitational force, $\left[G\right]=\left[M^{-1}{L}^3{T}^{-2}\right]$

The dimensional formula of

$\left[\frac{E{J}^2}{M^5{G}^2}\right]=\frac{\left[M^1{L}^2{T}^{-2}\right].[M^1{L}^2{T}^{-1}{]}^2}{\left[M^5\right][M^{-1}{L}^3{T}^{-2}{]}^2}$

$=\frac{\left[M^3{L}^6{T}^{-4}\right]}{\left[M^3{L}^6{T}^{-4}\right]}$

$\left[\frac{E{J}^2}{M^5{G}^2}\right]=\left[M^0{L}^0{T}^0\right]$

$\left(E{J}^2/M^2{G}^2\right)$ is a dimensionless quantity.

This comes out to be dimensionless and angle is also dimensionless.

Option D