The dimension 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 low of gravitation the force of attaction between two masses `m_(1) and m_(2)` respectively by a distance r is
`F = (Gm_(1)m_(2))/(r^(2)) rArr G = (Fr^(2))/(m_(1)m_(2))`
Substititing the dimensions for the quantities on the right hand sides we obatain dimension of
`G = ([MLT^(-2)][L^(2)])/(M^(2)] = [M^(-1) L^(1)T^(-2)]`