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A ball collides elastically with a uniform rod that is smoothly hinged at one end (point A). The ball strikes the rod at some point along its length. Which of the following statements about the collision are correct?
- Linear momentum of the system (ball + rod) is conserved during the collision.
- Angular momentum of the system about the hinge point A is conserved during the collision.
- The initial kinetic energy of the system equals the final kinetic energy of the system.
- The linear momentum of the ball alone is conserved during the collision.
Correct answer: Angular momentum of the system about the hinge point A is conserved during the collision.
Solution
The hinge at A exerts an external impulsive force on the system, so total linear momentum of the system is not conserved (eliminating options A and D). Since the hinge force acts at A, its torque about A is zero, so angular momentum about A is conserved (option B correct). The collision is elastic, so kinetic energy is conserved (option C correct). Correct answers: B and C.
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