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Inside a smooth hollow thin semicircular tube held in a vertical plane, a block of the same mass as the tube is released from rest at the top. When slightly disturbed it slides down and moves toward the right end of the tube. The whole system rests on a frictionless horizontal surface. By the time the block reaches the right end of the tube, what is the horizontal displacement of the tube? (R is the mean radius of the tube.)

1. R/2
2. 2R/pi
3. 4R/pi
4. R

Correct answer: R/2

Solution

With a frictionless floor the centre of mass has no horizontal motion; the block's horizontal displacement relative to the tube (top of arc to right end) is R, so for equal masses the tube moves half of it, R/2.

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