Question

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

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

Answer 1

The correct option is A time

Given formula is

$\frac{GI{M}^2}{E^2}$ where, G = Gravitational constant, I = Impulse, M = Mass, E = Energy

We have to find the dimensional formula for the given equation

We can write,

$\frac{GI{M}^2}{E^2}$=$\frac{\left[M^{-1}{L}^3{T}^{-2}\right]\left[ML{T}^{-1}\right]\left[M^2\right]}{{\left[M{L}^2{T}^{-2}\right]}^2}=\frac{\left[M^2{L}^4{T}^{-3}\right]}{\left[M^2{L}^4{T}^{-4}\right]}$

$=\left[M^0{L}^0{T}^1\right]$
From the above we can say that the dimension of the given equation is same as the dimension of the time.