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Two identical balls each of mass m inter...

Two identical balls each of mass m interconnected by a small light inextensible string are kept on a smooth horizontal surface. One of the balls is pushed towards the other with a speed `v_(0)` find the loss of K.E. of the ball. What will be the final velocities of the balls ? (e=1).

Text Solution

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We know that, when two identical bodies collide elastically, they transfer their momenta. That means, Just after collision the stationary ball starts moving with a speed `v_(0)` and the first ball will be stationary. The second ball will continue moving with speed, say, v. Since no external force is acting on the system of the balls and string (tension in the string is internal force), the system conserves its linear momentum. Conserving the momentum of the system just before and after the string taul obtain.
`mv_(0)=mv+mv`
`rArr v=(v_(0))/(2)`
(a) Now the loss in K.E. of the ball
`Delta KE=(1)/(2)m v^(2)+(1)/(2)mv^(2)-(1)/(2)mv_(0)^(2)`
Putting `v=(v_(0))/(2)`, value of `Delta KE` can be found.
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