Question

If the gravitational force F=GM1M2/r2 derive the dimension of the constant G.

Answer 1

Answer:

G is constant so it is dimensionless.

Answer 2

The dimensional formula of G is $[M^{-1}L^3T^{-2}]$

Explanation:

The force between two masses is given by :

$F=G\dfrac{m_1m_2}{r^2}$

$m_1\ and\ m_2$ are two masses

r is the distance between masses

On solving the above formula we get :

$G=\dfrac{Fr^2}{m^2}$

The dimensional formula of force is, $[F]=[MLT^{-2}]$

The dimensional formula of distance is, $[r]=[L]$

The dimensional formula of mass is, $[m]=[M]$

Putting in the above formula we get :

$[G]=\dfrac{MLT^{-2}{\cdot} L^2}{M^2}$

$[G]=[M^{-1}L^3T^{-2}]$

So, the dimensional formula of G is $[M^{-1}L^3T^{-2}]$

Learn more,

Dimensional formula

https://brainly.in/question/6006118