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

Moderate

A

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

$v = \sqrt{\frac{Gm}{2 R}}$
C

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

$v = \sqrt{\frac{4 Gm}{R}}$

Solution

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

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