What is the dimension of gravitational constant?

The correct answer is M-1L3T-2

Key Points

CONCEPT:

• Newton's law of gravitation states that any two bodies having masses (m₁ and m₂) keeping at a distance (r) from each other exerts a Force of attraction on each other.
  • This Force is directly proportional to the masses of bodies and inversely proportional to the square of the distance between them.
  • The dimension of the Force is MLS^-2 and the SI unit is Newton (N).

\(\Rightarrow F \propto \frac{m_1.m_2}{r^2}\Rightarrow F= \frac{Gm_1m_2}{r^2}\)

Here, G is the proportional Constant and its value is 6.674 x 10^-11 m³Kg^-1s^-2 is a universal constant.

SOLUTION:

• We can rewrite the above equation as: \(G = \frac{F r^2}{m_1m_2}\)

\(\Rightarrow Dimension \,of \,G = \frac{Kg m sec^{-2.}m^2}{Kg^2}= \frac{m^3 sec^{-2}}{Kg}\)

As we know, the dimension of length (meter) = L

Dimension of time (t) = T

Dimension of mass (kg) = M 

Therefore, the dimension of gravitational constant (G) is

\(\Rightarrow G = \frac{[L^3T^{-2}]}{[M]}=[M^{-1}L^3T^{-2}]\)

Hence, Dimension of Gravitational Constant G = M^-1L³T^-2.