The dimensionas of universal gravitational constant are ____

Options

A. `[M^(-1)L^(3)T^(-2)]`
B. `[ML^(2)T^(-1)]`
C. `[M^(-2)L^(3)T^(-2)]`
D. `[M^(-2)L^(2)T^(-1)]`

Answer

A

Explanation

According to Newton's law of gravitation, the force of attraction between two masses `m_(1)` and `m_(2)` separated by a distance r is,
`F = (G m_(1)m_(2))/(r^(2)) rArr G = (Fr^(2))/(m_(1)m_(2))`
Substituting the dimensions for the quantities on the right hand, side we obtain
Dimensions of `G = ([MLT^(-2)])/([M]^(2)) = [M^(=1)L^(3)T^(-2)]`