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A uniform disc of mass m and radius a is at rest on a smooth horizontal table with centre at C. A particle of mass m moving horizontally with speed v strikes the disc at a point on its rim and sticks to it. If the loss in kinetic energy of the system is written as m * v² / n, find the value of n.

1. (A) n = 12
2. (B) n = 6
3. (C) n = 4
4. (D) n = 3

Correct answer: (A) n = 12

Solution

After the perfectly inelastic collision, the particle (mass m) sticks to the rim of the disc (mass m). Conservation of linear and angular momentum gives v_cm = v/2 and omega = 2v/(3a). The initial KE is mv²/2. Computing the final KE and subtracting gives a loss of mv²/12, so n = 12.

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