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A horizontal frictionless rod is threade...

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?

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