JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Gravitation

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A body is released from a height equal to the radius (R) of the earth. The velocity of the body when it strikes the surface of the earth will be :
(Given

g =

acceleration due to gravity on the earth.)

(A) $g R$ ✓ Correct
(B) $4 g R$
(C) $2 g R$
(D) $\frac{g R}{2}$

Answer: (A)

Solution

Releasing the body from a height

R

places it a distance

2 R

from the Earth's centre. Energy conservation gives

- \frac{GM m}{2 R} = - \frac{GM m}{R} + \frac{1}{2} m v^{2}

, so

\frac{1}{2} m v^{2} = \frac{GM m}{2 R}

and

v = \frac{GM}{R}

. Using

g = \frac{GM}{R ^{2}}

, the speed at the surface is

g R

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Single correct option

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