Question

In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in the 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 ${}^{\prime }{R}^{\prime }$ is mean radius of tube). Assume that the tube remains in vertical plane. (Horizontal plane is smooth)

• A. $R$
• B. $2R/\pi$
• C. $4R/\pi$
• D. $R/2$

Answer 1

The correct option is D $R/2$

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

$mx=m(R-x)$

$x=\frac{R}{2}$