First slide

Gravitaional potential energy

Question

A body of mass m is released from a height equal to the radius R of the earth. What will be the velocity of the body when it strikes the surface of the earth?

Moderate

A

$\sqrt{gR}$
B

$\sqrt{2 gR}$
C

$2 \sqrt{gR}$
D

$\sqrt{\frac{gR}{2}}$

Solution

By conservation of mechanical energy
$- \frac{GMm}{2 R} + 0 = - \frac{GMm}{R} + \frac{1}{2} {mv}^{2} \Rightarrow v = \sqrt{\frac{GM}{R}} = \sqrt{\frac{GM}{R^{2}} R} = \sqrt{gR}$

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