JEE Main 2025 Apr 4 Shift 2, Physics Q9: Gravitational Potential, Potential Energy And Work Done

JEE Main2025Apr 4, Shift 2Physics

An object is kept at rest at a distance of $3 R$ above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume $M$ = mass of earth, $G$ = Universal gravitational constant)

A
$\frac{GM}{2 R}$
B
$\frac{GM}{R}$
C
$\frac{3 GM}{R}$
D
$\frac{2 GM}{R}$

Solution

The object sits at a distance $r = R + 3 R = 4 R$ from the earth's centre. Escape from this altitude requires the total mechanical energy to be at least zero:

$\frac{1}{2} m v^{2} - \frac{GM m}{4 R} = 0$

$\Rightarrow v_{m i n} = \frac{2 GM}{4 R} = \frac{GM}{2 R}$ .

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JEE Main 2025 Apr 4 Shift 2, Physics Q9: Gravitational Potential, Potential Energy And Work Done

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