Question

The dimensions of universal gravitational constant are:

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

From Universal law of gravitation, we know $F=\frac{GMm}{R^2}$, where, 'G' is the gravitational constant, 'M' is the mass of first object and 'm' is the mass of the second object and 'R' is the distance between them.
Therefore, $G=\frac{F\times R^2}{M\times m}$
Since it's S.I. unit is $\frac{N-m^2}{{kg}^2}$, therefore N is unit of force = $ML{T}^{-2}$​, dimension of length (m) = L , dimension of mass (kg) = M.
So, the dimensions of universal gravitational constant is $\frac{M{L}^3{T}^{-2}}{M^2}$ =$M^{-1}{L}^3{T}^{-2}$