Question

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

• A. $v=\frac{1}{2R}\sqrt{\frac{1}{Gm}}$
• B. $v=\sqrt{\frac{Gm}{2R}}$
• C. $v=\frac{1}{2}\sqrt{\frac{Gm}{R}}$
• D. $v=\sqrt{\frac{4Gm}{R}}$

Answer 1

The correct option is C $v=\frac{1}{2}\sqrt{\frac{Gm}{R}}$

Centripetal force is provided by the gravitational force of attraction between two particles.

ie, $\frac{m{v}^2}{R}=\frac{Gm\times m}{(2R{)}^2}$

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