Question

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

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

Answer 1

The Correct Option is A

$[ E ]= ML ^{2} T ^{-2}$
$[ G ]=\frac{\left[ Fr ^{2}\right]}{\left[ m _{1} m _{2}\right]}=\left[\frac{ ML T ^{-2} L ^{2}}{ M ^{2}}\right]= M ^{-1} L ^{3} T ^{-2}$
$\therefore\left[\frac{ E }{ G }\right]=\frac{ ML ^{2} T ^{-2}}{ M ^{-1} L ^{3} T ^{-2}}=\left[ M ^{2} L ^{-1} T ^{0}\right]$