Question

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of

• A. $\left[M^2\right]\left[L^{–2}\right]\left[T^{–1}\right]$
• B. $\left[M^2\right]\left[L^{–1}\right]\left[T^0\right]$
• C. $\left[M\right]\left[L^{–1}\right]\left[T^{–1}\right]$
• D. $\left[M\right]\left[L^0\right]\left[T^0\right]$

Answer 1

The correct option is B $\left[M^2\right]\left[L^{–1}\right]\left[T^0\right]$

Dimensional formula of energy

$\left[E\right]=\left[M^1{L}^2{T}^{-2}\right]...\left(1\right)$

Dimensional formula of gravitational constant,

$\left[G\right]=\left[M^1{L}^3{T}^{-2}\right]...\left(2\right)$

From equations $\left(1\right)\&\left(2\right)$,

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

$=\left[M^2{L}^{-1}{T}^0\right]$

Hence, dimensions of $\left[\frac{E}{G}\right]$ is $\left[M^2\right]\left[L^{-1}\right]\left[T^0\right]$.

So, correct option is $\left(\text{B}\right)$.