A metallic bob X of mass m is released from position A. It collides elastically with another identical bob Y placed at rest at position B on a horizontal frictionless table. The angle AOB is 30°. How high does the bob X rise immediately after the collision ?

The behavior of the bobs is governed by the principles of elastic collision in one dimension. When two bodies of equal mass collide elastically, they exchange their velocities.

• Before Collision: Bob X (mass m) reaches position B with a specific velocity, while Bob Y (mass m) is at rest (velocity = 0).
• During Collision: Because the collision is elastic and the masses are identical, Bob X transfers its entire linear momentum and kinetic energy to Bob Y.
• After Collision: Bob X takes on the initial velocity of Bob Y (which was zero) and comes to a complete stop at position B. Conversely, Bob Y takes on the velocity Bob X had just before impact and moves forward.

Since Bob X has zero velocity immediately after the collision, it cannot rise along any trajectory. Thus, Option D is correct.