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

A $[M][L^{-1}][T^{-1}]$

B $[M][L^0][T^0]$

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

D $[M^2][L^{-1}][T^0]$

The answer is D.

Solution

$[E] = [ML^2T^{-2}]$ ; $[G] = [M^{-1}L^3T^{-2}]$ $\frac{[E]}{[G]} = \frac{ML^2T^{-2}}{M^{-1}L^3T^{-2}} = [M^2L^{-1}T^0]$

Concept dimensions of E/G

3 questions from this chapter have appeared across 3 exam years.