Question

A bullet having some initial velocity $v_B$ hits a ballistic pendulum of mass $m_B$ and lodges in it. When the bullet hits the pendulum it swings up from the equilibrium position and rises up to height $h$ as shown in figure.

Choose correct option.

• A. Kinetic energy of bullet before collision will be same as potential energy of (bullet+pendulum) at height $h$.
• B. Kinetic energy of (bullet+pendulum) after collision will be same as potential energy of (bullet+pendulum) at height $h$.
• C. Collision between bullet and pendulum is completely elastic.
• D. None of these

Answer 1

The correct option is A Kinetic energy of bullet before collision will be same as potential energy of (bullet+pendulum) at height $h$.

As given in question bullet lodges to pendulum after collision. Therefore collision is perfectely inelastic.

We know in perfectely inelastic collision there is some loss of kinetic energy due to deformation of object.
$\therefore$Kinetic energy of (bullet+pendulum) after collision is less than the initial kinetic energy of bullet.

After collision, according to law of conservation of energy, K.E of (bullet +pendulum) will be equal to the P.E of (bullet +pendulum) at height $h$ as there is no non conservative forces.