Question

Two particles of equals mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction . The speed of each prticle with respect to their centre of mass is :-

• A. $\sqrt{\frac{Gm}{R}}$
• B. $\sqrt{\frac{Gm}{4R}}$
• C. $\sqrt{\frac{Gm}{3R}}$
• D. $\sqrt{\frac{Gm}{2R}}$

Answer 1

The correct option is B $\sqrt{\frac{Gm}{4R}}$

When the particles of mass m are moving in a circle of radius R then the centripetal force balances the gravitation attraction as

$\frac{m{v}^2}{R}=\frac{G{m}^2}{{\left(2R\right)}^2}$

$v^2=\frac{Gm}{4R}$

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

Velocity of each particle is $\sqrt{\frac{Gm}{4R}}$