First slide

Motion of planets and satellites

Question

The escape velocity from the centre of a uniform ring of mass M and radius R is

Moderate

A

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

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

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

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

Solution

$\frac{1}{2} {mv}^{2} - \frac{GMm}{R} = 0 \Rightarrow v = \sqrt{\frac{2 GM}{R}}$

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