Question

Two identical particles each of mass \( m \) go around a circle of radius \( a \) under the action of their mutual gravitational attraction. The angular speed of each particle will be:

• A. \( \sqrt{\frac{Gm}{2a^3}} \)
• B. \( \sqrt{\frac{Gm}{8a^3}} \)
• C. \( \sqrt{\frac{Gm}{4a^3}} \)
• D. \( \sqrt{\frac{Gm}{a^3}} \)

Hint:

When solving problems involving gravitationally bound circular motion, simplify by expressing the gravitational force in terms of the centripetal force. Keep track of distances, as they directly impact force calculations.