A horizontal frictionless rod is threaded through a bead of mass `m`. The length of the cart is `L` and the radius of the bead, `r`, is very small in comparison with `L(r lt lt L)`. Initially at (`t = 0`) the bead is at the right edge of the cart. The can is struck and as a result, it moves with velocity `v_(0)` towards right. When the bead collides with the cart's walls, the collisions are always completely elastic.

What is the velocity of the cart just after the first collision?

Options

A. `(-mv_(0))/(m+M)`
B. `(Mv_(0))/(m+M)`
C. `(M-m)/(M+m)v_(0)`
D. `(2M)/(m+M)v_(0)`

Answer

C

Explanation

`Mv_(0)=Mv_(1)+mv_(2)`…………i
`(v_(2)-v_(1))/(v_(0))=`………..ii
Solve to get `v_(1)=(M-m)/(M+m)v_(0)`
`v_(2)=(2M)/(m+M)v_(0)`