JEE Main 2026 Apr 5 Shift 2, Physics Q7: Gravitational Potential, Potential Energy And Work Done

JEE Main2026Apr 5, Shift 2Physics

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ( $R_{e}$ ). The increase in potential energy will be _____. ( $g$ is acceleration due to gravity at the surface of earth)

A
$\frac{1}{2} m g R_{e}$
B
$\frac{3}{4} m g R_{e}$
C
$\frac{1}{4} m g R_{e}$
D
$\frac{2}{3} m g R_{e}$

Solution

Potential energy at the surface: $U_{1} = - \frac{GM m}{R _{e}}$ .

At height $2 R_{e}$ (so distance from centre $= 3 R_{e}$ ): $U_{2} = - \frac{GM m}{3 R _{e}}$ .

$Δ U = U_{2} - U_{1} = - \frac{GM m}{3 R _{e}} + \frac{GM m}{R _{e}} = \frac{2}{3} \cdot \frac{GM m}{R _{e}}$ .

Using $g = GM / R_{e}^{2}$ , this becomes $\frac{2}{3} m g R_{e}$ .

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JEE Main 2026 Apr 5 Shift 2, Physics Q7: Gravitational Potential, Potential Energy And Work Done

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