A ball of mass `m` is moved with speed `v_0` at the highest point in a closed circular tube of radius `R` kept in the vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.

Explanation

`K_1+U_1=K_2+U_2+W_f`
`(1)/(2)mv_0^2+mgxx2R=0+0+Wf`
Work done by friction
`W_f^(')=-W_f=-[(1)/(2)mv_0^2+2mgR]`