First slide

Gravitational force and laws

Question

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

Easy

A

$v = \frac{1}{2 R} \sqrt{\frac{1}{G m}}$
B

$v = \sqrt{\frac{G m}{2 R}}$
C

$v = \frac{1}{2} \sqrt{\frac{G m}{R}}$
D

$v = \sqrt{\frac{4 G m}{R}}$

Solution

Centripetal force provided by the gravitational force of attraction between two particles
$i . e . \frac{m v^{2}}{R} = \frac{G m \times m}{{(2 R)}^{2}} \Rightarrow v = \frac{1}{2} \sqrt{\frac{G m}{R}}$

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