Q. The dimensions of gravitational constant $G$ and the moment of inertia are respectively
A) $\left\lbrack ML^{3}T^{- 2} \right\rbrack;\left\lbrack ML^{2}T^{0} \right\rbrack$
B) $\left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack;\left\lbrack {ML}^{2}T^{0} \right\rbrack$
C) $\left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack;\left\lbrack M^{- 1}L^{2}T \right\rbrack$
D) $\left\lbrack {ML}^{3}T^{- 2} \right\rbrack;\left\lbrack M^{- 1}L^{2}T \right\rbrack$
Explanation
$F = \frac{Gm_{1}m_{2}}{d^{2}}$ $\Rightarrow \ \ G = \frac{Fd^{2}}{m_{1}m_{2}}$ $\ \ \ \ \lbrack G\rbrack = \frac{\left\lbrack MLT^{- 2} \right\rbrack\lbrack L^{2}\rbrack}{\left\lbrack M^{2} \right\rbrack} = \left\lbrack M^{- 1}L^{3}T^{2} \right\rbrack$ Moment of inertia $I = mK^{2} = \left\lbrack {ML}^{2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.