If G is the gravitational constant and u is t | vedclass

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(B) The dimension of energy density $u$ is $[M^1 L^{-1} T^{-2}]$.The dimension of gravitational constant $G$ is $[M^{-1} L^3 T^{-2}]$.Therefore,the di

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Force per unit mass

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(B) The dimension of energy density $u$ is $[M^1 L^{-1} T^{-2}]$.The dimension of gravitational constant $G$ is $[M^{-1} L^3 T^{-2}]$.Therefore,the dimension of $uG$ is $[M^1 L^{-1} T^{-2}] 	imes [M^{-1} L^3 T^{-2}] = [M^0 L^2 T^{-4}]$.Taking the square root,the dimension of $\sqrt{uG}$ is $[L^1 T^{-2}]$.This dimension $[L T^{-2}]$ corresponds to acceleration.Force per unit mass is given by $F/m = ma/m = a$,which has the dimension $[L T^{-2}]$.Thus,option $B$ is correct.

If $G$ is the gravitational constant and $u$ is the energy density,then which of the following quantities has the same dimensions as $\sqrt{uG}$?

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