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

Question

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

Accepted Answer

The dimensional formula for energy ($E$) is $[ML^2T^{-2}]$.
The dimensional formula for the universal gravitational constant ($G$) is $[M^{-1}L^3T^{-2}]$.
Now, substituting these dimensions into the given expression $\frac{E}{G}$:
$\left[\frac{E}{G}\right] = \frac{[ML^2T^{-2}]}{[M^{-1}L^3T^{-2}]}$
$\left[\frac{E}{G}\right] = [M^{1 - (-1)} L^{2 - 3} T^{-2 - (-2)}]$
$\left[\frac{E}{G}\right] = [M^2 L^{-1} T^0]$.
Thus, the correct dimensional formula is $[M^2L^{-1}T^0]$.

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