Question

If G be the gravitational constant and u be thee nergy density then which of the following quantity have the dimension as that the \(\sqrt{UG}\)

• A. Pressure gradient per unit mass
• B. Force per unit mass
• C. Gravitational potential
• D. Energy per unit mass

Answer 1

The Correct Option is B

Dimensional analysis:

\[ [uG] = \left( M^1L^{-1}T^{-2} \right) \times \left( M^{-1}L^2T^{-3} \right) = \left[ M^2L^2T^{-4} \right] \]

\[ \sqrt{uG} = \left[ M^1L^1T^{-2} \right] \]

This corresponds to the dimensions of force per unit mass. Therefore, Option (2) is correct.