If \(G\) be the gravitational constant and u be the energy density then which of the following quantity have the dimensi…

Explanation

Dimension of energy density:

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

Dimension of gravitational constant:

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

Multiply the dimensions:

\([\mathrm{uG}]={M}^{0}{L}^{2}{T}^{-4}\)

Take square root:

\([\sqrt{\mathrm{uG}}]=L{T}^{-2}\)

Dimension of force per unit mass:

\([\frac{\text{Force}}{\text{Mass}}]=ML{T}^{-2}M\) \([\frac{\text{Force}}{\text{Mass}}]=L{T}^{-2}\)

Hence, the required quantity is force per unit mass.