Question

If $E, m, J$ and $G$ represent energy, mass, angular momentum and gravitational constant respectively, then the dimensional formula of $E J^{2} / m^{5} G^{2}$ is

• A. angle
• B. length
• C. mass
• D. time

Answer 1

Answer: (A)

$[E]= ML ^{2} T ^{-2}$
$[J]=[$ Moment of Inertia $] \times[$ Angular velocity $]$
$= ML ^{2} T ^{-1}$
$[G]=\left[\frac{F \cdot r^{2}}{M \cdot m}\right]=\frac{ MLT ^{-2} \cdot L ^{2}}{ M ^{2}}= M ^{-1} L ^{3} T ^{-2}$
Hence, $\left[\frac{E J^{2}}{m^{5} G^{2}}\right]=\frac{\left[ ML ^{2} T ^{-2}\right] \cdot\left[ ML ^{2} T ^{-1}\right]^{2}}{\left[ M ^{5}\right] \cdot\left[ M ^{-1} L ^{3} T ^{-2}\right]^{2}}$
$= M ^{0} L ^{0} T ^{0}=[$ angle $]$