A speeding bullet collides with and embeds into a pendulum bob. As a result, the

Question

A speeding bullet collides with and embeds into a pendulum bob. As a result, the pendulum bob and embedded bullet swing to a maximum height. The kinetic energy of the bullet is equal to the potential energy of the pendulum bob and embedded bullet at the maximum height. The momentum of the speeding bullet is equal to the momentum of the pendulum bob and embedded bullet immediately after the collision. The kinetic energy of the speeding bullet is equal to the kinetic energy of the pendulum bob and embedded immediate after the collision. The momentum of the speeding bullet is greater than the momentum of the pendulum bob and embedded bullet just after the collision.

Explanation / Answer

To answer this question, we have to first understand about different types of collisions between two particles.

If the collision between two bodies is an elastic collision, then the kinetic energy of system before collision will be equal to the kinetic energy of system after the collision.

If the collision between two bodies is inelastic collision, then the kinetic energy of system before collision will more than kinetic energy of the system after collision

If the collision between two bodies is perfectly inelastic, then again, the kinetic energy of the system before collision will be more than the kinetic energy of the system after the collision.

Therefore in both inelastic and perfectly inelastic collisions, there is loss of mechanical energy in the form of heat and sound.

A perfectly inelastic collision is a collision in which the colliding bodies stick to each other after the collision and start moving together. Since the bullet and pendulum bob move together after the collision. The collision happening in the question is a perfectly inelastic collision.

Therefore in the collision between bullet and pendulum some mechanical energy of the system is lost as heat and sound. So, option A and option C are wrong.

Now, During any type of collision, there is no external force on the system and, from the law of conservation of momentum, momentum will be covered in any type of collision. That means, the momentum of the system before the collision is equal to the momentum of the system after collison.

Here, from the question, the initial momentum of the system before the collision is same as the momentum of the bullet (as the pendulum bob is at rest before collision). After the collision, the bullet gets embedded in pendulum bob and they move together. So, momentum of the system is the momentum of bullet and pendulum bob as system.

From law of conservation of momentum, we can say that the momentum of bullet is equal to the momentum of pendulum bob and embedded bullet immediately after collision.

Therefore, option B is the correct choice.

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