Solve this following
Question:

If $\mathrm{E}, \mathrm{L}, \mathrm{M}$ and $\mathrm{G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of $P$ in the formula $\mathrm{P}=\mathrm{EL}^{2} \mathrm{M}^{-5} \mathrm{G}^{-2}$ are :-

1. $\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{0}\right]$

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

3. $\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$

4. $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$

Correct Option: , 4

Solution:

$\mathrm{E}=\mathrm{ML}^{2} \mathrm{~T}^{-2}$

$\mathrm{L}=\mathrm{ML}^{2} \mathrm{~T}^{-1}$

$\mathrm{m}=\mathrm{M}$

$\mathrm{G}=\mathrm{M}^{-1} \mathrm{~L}^{+3} \mathrm{~T}^{-2}$

$\mathrm{P}=\frac{\mathrm{EL}^{2}}{\mathrm{M}^{5} \mathrm{G}^{2}}$

$[\mathrm{P}]=\frac{\left(\mathrm{ML}^{2} \mathrm{~T}^{-2}\right)\left(\mathrm{M}^{2} \mathrm{~L}^{4} \mathrm{~T}^{-2}\right)}{\mathrm{M}^{5}\left(\mathrm{M}^{-2} \mathrm{~L}^{6} \mathrm{~T}^{-4}\right)}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$

Option (4)