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.
Velocity of `A` immediately after collision is along unit vector

Options

A. `hatj`
B. `1/2hati+sqrt(3)/2hatj`
C. `hatj`
D. none of these

Answer

B

Explanation

velocity of `A:vecv_(1)=v_(1)costhetahati+v_(1)sinthetahatj`
`impliesvecv_(1)=costhetahati+sinthetahatj=1/2hati+(sqrt(3))/2hatj`