Question

The two particles of equal mass $\text{m}$ go round a circle of radius $\text{R}$ under the action of their mutual gravitational attraction. The speed of each particle is :

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

Answer 1

The correct option is C

$\frac{1}{2}\sqrt{\frac{Gm}{R}}$
Centripetal force provided by gravitational force of attraction between two particles,

$\frac{m{v}^2}{R}=\frac{G{m}^2}{4R^2}$
$\Rightarrow v=\sqrt{\frac{Gm}{4R}}$
$\Rightarrow v=\frac{1}{2}\sqrt{\frac{Gm}{R}}$