Q. If $E,m,J$ and $G$ represent energy, mass, angular momentum and gravitational constant respectively, then the dimensional formula of $EJ^{2}$/$m^{5}G^{2}$ is
A) $\lbrack MLT^{- 2}\rbrack$
B) $\lbrack M^{0}L^{0}T\rbrack$
C) $\lbrack M^{0}L^{2}T^{0}\rbrack$
D) Dimensionless
Explanation
$\frac{\lbrack E\rbrack\lbrack J\rbrack^{2}}{\lbrack M\rbrack^{5}\lbrack G\rbrack^{2}}\frac{\left\lbrack ML^{2}T^{- 2} \right\rbrack\left\lbrack ML^{2}T^{- 1} \right\rbrack^{2}}{\left\lbrack M^{5} \right\rbrack\left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack^{2}} = \lbrack M^{0}L^{0}T^{0}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.