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Q.

In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed it moves towards right. By the time the block reaches the right end of the tube then the displacement of the tube will be (where R is mean radius of tube). Assume that the tube remains in vertical plane and friction is absent everywhere.

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a

$\frac{2 R}{π}$

b

$\frac{4 R}{π}$

c

$\frac{R}{2}$

d

R

answer is C.

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Detailed Solution

Let the tube displaced by x towards left, then block will be displaced by $(R - x)$ towards right;

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$mx = m (R - x) \Rightarrow x = \frac{R}{2}$

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In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed it moves towards right. By the time the block reaches the right end of the tube then the displacement of the tube will be (where R is mean radius of tube). Assume that the tube remains in vertical plane and friction is absent everywhere.