Question

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

• A. \( \sqrt{\frac{GM}{R}} \)
• B. \( \sqrt{\frac{GM}{R^2}} \)
• C. \( \sqrt{\frac{GM}{R^3}} \)
• D. \( \sqrt{\frac{GM}{R}} \)

Hint:

For two bodies under mutual gravitational attraction in circular motion, the centripetal force is provided by the gravitational force.

Answer 1

The Correct Option is A

Step 1: Gravitational force and circular motion.
The gravitational force provides the centripetal force for the circular motion of the particles. By equating the gravitational force to the centripetal force, we can solve for the speed of the particles.

Step 2: Conclusion.
The speed of each particle is \( \sqrt{\frac{GM}{R}} \), which corresponds to option (1).