Question

As shown below, bob A of a pendulum having a massless string of length \( R \) is released from 60° to the vertical. It hits another bob B of half the mass that is at rest on a frictionless table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take \( g \) as acceleration due to gravity):

• A. \( \frac{1}{3} \sqrt{Rg} \)
• B. \( \sqrt{Rg} \)
• C. \( \frac{2}{3} \sqrt{Rg} \)
• D. \( \frac{4}{3} \sqrt{Rg} \)

Hint:

In problems involving elastic collisions, use both conservation of energy and conservation of momentum to solve for unknown velocities.

Answer 1

The Correct Option is C

In an elastic collision, the velocities of the objects are related by the conservation of momentum and energy. For bob A, the velocity after collision can be derived using the principles of energy and momentum conservation, and the result is \( \frac{2}{3} \sqrt{Rg} \).