Question

Paragraph for Question Nos. 23 to 25

A smooth disc of mass M and radius R can rotate freely around a vertical axis supported by frictionless bearings. A constraining vertical surface of negligible mass, whose shape is a semicircular arc of radius $r=\frac{R}{2}$, is fixed on the disc as shown in the figure. A small ball of mass m is placed on the stationary disc and is bowled at a speed v in such a way that it reaches the internal side of the constraining surface tangentially.

23. Mark the CORRECT statement :-

• A. Momentum of ball & disc system is conserved
• B. Mechanical energy of ball & disc system is not conserved
• C. Angular momentum of ball & disc system is conserved
• D. Mechanical energy of ball & disc system is not conserved due to impulsive reaction from support bearings

Answer 1

Answer: (C)

Angular momentum of ball & disc system is conserved

Answer 2

The system of the ball and the disc rotates about a fixed vertical axis. The external forces acting on the system (gravity, normal force from support) produce no torque about this axis. Internal forces between the ball and the constraint also produce no net torque about this axis. Therefore, the total angular momentum of the system about the vertical axis is conserved. Linear momentum is not conserved due to external forces from the support. Mechanical energy is conserved if there are no non-conservative forces like friction or inelastic collisions. Given "smooth disc" and "frictionless bearings", energy conservation is likely intended, but option (B) states it is not conserved. Option (C) is the most definitively correct statement based on the problem description.