PYQ NEET- Units Of Measurement L-9

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

A) $\left[\mathrm{M}^2\right]\left[\mathrm{L}^{-2}\right]\left[\mathrm{T}^{-1}\right]$

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

C) $[\mathrm{M}]\left[\mathrm{L}^{-1}\right]\left[\mathrm{T}^{-1}\right]$

D) $[M]\left[L^0\right]\left[T^0\right]$

Answer: $[M]\left[L^0\right]\left[T^0\right]$#

Solution:#

$\mathrm{E}=$ energy $=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$

$\mathrm{G}=$ Gravitational constant $=\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$

So, $\frac{E}{G}=\frac{[E]}{[G]}=\frac{M L^2 T^{-2}}{M^{-1} L^3 T^{-2}}=\left[M^2 L^{-1} T^0\right]$