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JEE Main 20245 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 5 April
Shift: Morning Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2024 · 5 April · Morning Shift · Physics · Units and Dimensions

If G be the gravitational constant and u be the energy density then...

If

\mathrm{G}

be the gravitational constant and

\mathrm{u}

be the energy density then which of the following quantity have the dimensions as that of the

\sqrt{\mathrm{uG}}

:

Options

Apressure gradient per unit mass
BGravitational potential
CEnergy per unit mass
DForce per unit mass

Correct answer

D. Force per unit mass

Step-by-step solution

\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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