MCQ
If $\mathrm{E}$ and $\mathrm{G}$ respectively denote energy and gravitational constant, then $\frac{\mathrm{E}}{\mathrm{G}}$ has the dimensions of :
  • A
    $[\mathrm{M}]\left[\mathrm{L}^{-1}\right]\left[\mathrm{T}^{-1}\right]$
  • $\left[\mathrm{M}^{2}\right]\left[\mathrm{L}^{-1}\right]\left[\mathrm{T}^{0}\right]$
  • C
    $[\mathrm{M}]\left[\mathrm{L}^{0}\right]\left[\mathrm{T}^{0}\right]$
  • D
    $\left[\mathrm{M}^{2}\right]\left[\mathrm{L}^{-2}\right]\left[\mathrm{T}^{-1}\right]$

Answer

Correct option: B.
$\left[\mathrm{M}^{2}\right]\left[\mathrm{L}^{-1}\right]\left[\mathrm{T}^{0}\right]$
b
$E=$ energy $=\left[M L^{2} T^{-2}\right]$

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

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

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