Question

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

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

Answer 1

Answer: (A)

time

Answer 2

Dimensions of $E=\left[M L^{2}\, T^{-2}\right]$
Dimensions of $G=\left[M^{-1} \,L^{3} \,T^{-2}\right]$
Dimensions of $I=\left[M L\, T^{-1}\right]$
and dimensions of $M=[M]$
So, dimensions of $\frac{G IM ^{2}}{E^{2}}$
$=\frac{[G][I]\left[M^{2}\right]}{\left[E^{2}\right]}$
Substituting the dimensions for each physical quantity, we get
Dimensions of $\frac{G I M^{2}}{E^{2}}$
$=\frac{\left[M^{-1} \,L^{3} \,T^{-2}\right]\left[M L\, T^{-1}\right]\left[M^{2}\right]}{\left[M L^{2}\, T^{-2}\right]^{2}}$
$=[T]$
$=$ Dimensions of time