If G be the gravitational constant and u be thee nergy density then which of the following quantity have the dimension as that the \(\sqrt{UG}\)
- Pressure gradient per unit mass
- Force per unit mass
- Gravitational potential
- Energy per unit mass
The Correct Option is B
Solution and Explanation
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.
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