First slide

Gravitaional potential energy

Question

With what velocity should a particle be projected so that its height becomes equal to radius of earth?

Moderate

A

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

$\sqrt{\frac{8 GM}{R}}$
C

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

$\sqrt{\frac{4 GM}{R}}$

Solution

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

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