If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the

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Solution

Q.
If $G$ be the gravitational constant and $u$ be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{u G} .$ [2024]

1 Force per unit mass

2 Gravitational potential

3 pressure gradient per unit mass

4 Energy per unit mass

Ans.
(1)

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

$[u G] = [M^{0} L^{2} T^{- 4}]$

$[\sqrt{u G}] = [L^{1} T^{- 2}]$

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