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

• 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. $v=\sqrt{\frac{4 G m}{R}}$

Answer 1

Answer: (C)

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

i.e. $\frac{m v^{2}}{R}=\frac{G m \times m}{(2 R)^{2}}$
$\Rightarrow v=\frac{1}{2} \sqrt{\frac{G m}{R}}$