Three spheres, each of mass `m`, can slide freely on a frictionless, horizontal surface. Spheres `A` and `B` are attached to an inextensible, inelastic cord of length `l` and are at rest in the position shown where sphere `B` is struck by sphere `C` which is moving to the right with a velocity `v_(0)`. Knowing that the cord is taut where sphere `B` is struck by sphere `C` and assuming 'head on' inelastic impact between `B` and `C`, we cannot conserve kinetic energy of the entire system.
The velocity of `B` immediately after collision is along unit vector

Options

A. `(17mv_(0)^(2))`
B. `(15mv_(0)^(2))/64`
C. `(212mv_(0)^(2))/25`
D. none of these

Answer

A

Explanation

From eqn ii and iii we get
`(mv_(0))/2sintheta=mv_(2)impliesv_(2)=(sqrt(3v_(0)))/4`
Loss in `KE =1/2mv_(0)^(2)-[1/2m(v_(0)/2)^(2)+1/2mv_(1)^(2)+1/2mv_(1)^(2)+1/2mv_(2)^(2)]`
Put the values to get in `KE =17/64mv_(0)^(2)`