Question

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

• A. $\left[ M ^{0} \,L ^{1}\, T ^{0}\right]$
• B. $\left[ M ^{-1}\, L ^{-1} \,T ^{2}\right]$
• C. $\left[ M ^{1}\, L ^{1} \,T ^{-2}\right]$
• D. $\left[ M ^{0} \,L ^{0} \,T ^{0}\right]$

Answer 1

Answer: (D)

$E = ML ^{2} T ^{-2}$
$L = ML ^{2} T ^{1}$
$m = M$
$G = M ^{-1} L ^{+3} T ^{-2}$
$P =\frac{ EL ^{2}}{ M ^{5} G ^{2}}$
$[ P ]=\frac{\left( ML ^{2} T ^{-2}\right)\left( M ^{2} L ^{4} T ^{-2}\right)}{ M ^{5}\left( M ^{-2} L ^{6} T ^{-4}\right)}$
$= M ^{0} L ^{0} T ^{0}$