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 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.

• A. $\frac{2R}{\pi }$
• B. $\frac{4R}{\pi }$
• C. $\frac{R}{2}$
• D. R

Answer 1

The correct option is A $\frac{2R}{\pi }$

displacement of the center of mass

${△X}_{cm}=\frac{m_1△x_1+m_2△x_2}{m_1+m_2}$

Displacement of semicircle wire =x

Displacement of block in tube =r-x

$0=\frac{m_1△x_1+m_2△x_2}{m_1+m_2}$

$m_1△x_1=m_2△x_2$

$m\times (R-x)+m(-x)=0$

$(R-x)+(-x)=0$

$2x=R$

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