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.

If velocity of `C` immediately after collision becomes `(v_(0))/2` in the initial direction of motion, the impulse due to string on sphere `A` is

Options

A. `(mv_(0))/8`
B. `(mv_(0))/2`
C. `sqrt((mv_(0))/4`
D. none of these

Answer

A

Explanation

`For `C`: J=mv_(0)-(mv_(0))/2impliesJ=(mv_0)/2`…………..iii
Impulse on `A` due to string:
`J_(1)=mv_(1)=J/2costhetaimpliesJ_(1)=(mv_(0))/2 (costheta)/2=(mv_(0))/8`