A bullet of mass m and speed v hits a pendulum bob of mass M at time t₁, and passes completely through the bob. The bullet emerges at time t₂ with a speed of v/2. The pendulum bob is suspended by a stiff rod of length l and negligible mass. After the collision, the bob can barely swing through a complete vertical circle. At time t₃, the bob reaches the highest position.
What quantities are conserved in this process?
(a) Total kinetic energy of the bob and the bullet during the time interval Δt = t₂ – t₁.
(b) Total momentum of the bob and the bullet during the time interval Δt = t₂ - t₁.
(c) Total mechanical energy of the bob and the bullet during the time interval t₃ – t₁.
(d) Momentum of the bob after t₂.