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A block of mass with a semicircular track of radius rests on a horizontal frictionless surface. A uniform cylinder of radius and mass is released from rest from the top point . The cylinder slips on the semicircular frictionless track. The speed of the block when the cylinder reaches the bottom of the track at is

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The correct answer is:
Let the speed of the block be . Then from conservation of momentum, the velocity of the cylinder will be in the opposite direction
Now from conservation of energy
so
Now from conservation of energy
so
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