A ball of mass makes head-on elastic collision with a ball of mass which is initially at rest. Show that the fractional transfer of energy by the first ball is . Deduce the value of for which the transfer is maximum

Question ID - 101432 :-

A ball of mass makes head-on elastic collision with a ball of mass which is initially at rest. Show that the fractional transfer of energy by the first ball is . Deduce the value of for which the transfer is maximum

1 Answer

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Answer Key : (1) -

(1)

Let be the initial velocity of the ball of mass . Then

(i)

For elastic collision, Newton’s experimental formula is

(ii)

Solving Eqs. (i) and (ii),

Fractional loss in KE (= fractional transfer of KE)

The transfer of energy is maximum when or

This is, the transfer of energy is maximum when the mass ratio is unity

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