Units & Dimensions

JEE Main level, single correct, medium

58 of 149

Question 58 of 149

If G\mathrm{G} be the gravitational constant and u\mathrm{u} be the energy density then which of the following quantity have the dimensions as that of the uG\sqrt{\mathrm{uG}} :

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Answer: (D) Force per unit mass

[uG]=[(M1 L−1 T−2)(M−1 L3 T−2)][uG]=[M0 L2 T−4][uG]=[L1 T−2]\begin{aligned} & {[\mathrm{uG}]=\left[\left(\mathrm{M}^1 \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right)\left(\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right)\right]} \\ & {[\mathrm{uG}]=\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-4}\right]} \\ & {[\sqrt{\mathrm{uG}}]=\left[\mathrm{L}^1 \mathrm{~T}^{-2}\right]} \end{aligned}

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