Question

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

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

Answer 1

Answer: (A)

time

Answer 2

$E=\left[ML^{2}T^{-2}\right], G=\left[M^{-1}L^{3}T^{-2}\right]$, $I=\left[MLT^{-1}\right]$ $\therefore \frac{GIM^{2}}{E^{2}}=\frac{\left[M^{-1}L^{3}T^{-2}\right]\left[MLT^{-1}\right]\left[M^{2}\right]}{\left[ML^{2}T^{-2}\right]^{2}}=\left[T\right]$