Q. If $E =$ energy, $G =$ gravitational constant, $I =$ impulse and $M =$ mass, then dimensions of $\frac{GIM^{2}}{E^{2}}$ are same as that of

A) Time
B) Mass
C) Length
D) Force
Explanation

Dimensions of $E = \left\lbrack ML^{2}T^{- 2} \right\rbrack$ Dimensions of $G = \left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack$ Dimensions of $I = \left\lbrack MLT^{- 1} \right\rbrack$ And dimension of $M = \lbrack M\rbrack$ $\therefore Dimensions\ of\frac{GIM^{2}}{E^{2}} = \frac{\left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack\left\lbrack MLT^{- 1} \right\rbrack\left\lbrack M^{2} \right\rbrack}{\left\lbrack ML^{2}T^{- 2} \right\rbrack^{2}}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \lbrack T\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = Dimensions\ of\ time$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.