Question

A pendulum consist of a wooden bob of mass m and length l a bullet of mass m1 is fired towards the pendulum with a speed v1 the bullet emerges out of the Bob with the speed V1/3 and the Bob just completes motion along a vertical circle then V1 is

Answer 1

Given:

Wooden bob:

• Mass m
• Length l

Bullet:

• Mass m1
• Speed v1
• Bullet emerges out of the Bob v1/3
• Bob just completes motion along a vertical circle v1

Solution:

Kinetic Energy = 1/2 mv^2

Loss in Kinetic Energy of the bullet = 1/2 m1 (v1/3)^2

In order to make a complete circle of the bob,

√5gl

Where,

g is gravity.

1/2 m (√5gl)^2

Then,

v1 = 3/2 (m/m1) √5gl