Question

If G is universal gravitation constant and g is acceleration due to gravity, then dimensions of $G$ will be

• A. $\left[M^1{L}^{2}T\right]$
• B. $\left[M^{-1}{L}^3{T}^{-2}\right]$
• C. $\left[M^{2}LT\right]$
• D. $\left[M^1{L}^3{T}^{-2}\right]$

Answer 1

Answer: (B)

$\left[M^{-1}{L}^3{T}^{-2}\right]$

Force of attraction between two masses $M_{1}and{M}_2$ having separation $R$

$F=G\frac{M_1{M}_2}{R^2}$

$\left[ML{T}^{-2}\right]=G\left[M^2{L}^{-2}\right]$

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

Hence, dimention of $G$ is $\left[M^{-1}{L}^3{T}^{-2}\right]$