First slide

Gravitaional potential energy

Question

Given that mass of earth is M and its radius is R. A body is dropped from a height equal to the radius of earth above the surface of earth. When it reaches the ground, its speed will be:

Moderate

A

$\sqrt{\frac{GM}{R}}$
B

$\sqrt{\frac{GM}{2 R}}$
C

$\sqrt{\frac{2 Gm}{R}}$
D

$\frac{2 Gm}{R}$

Solution

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

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