(i) Three balls 1, 2 and 3 lie on a smooth horizontal table. Ball 1 is given a velocity towards ball 2. Kinetic energy given to ball 1 is `k_(0)`. It collides with 2 and in turn ball 2 hits ball 3. All collisions are head on elastic. Masses of the balls are m, M and m respectively.

(a) Calculate the kinetic energy `(k_3)` of ball 3 after ball 2 hits it.
(b) Draw the variation of `k_(3)` as a function of M.
(ii) Consider 10 balls laid on a smooth surface with masses `m,(m)/(2),(m)/(4),(m)/(8)......(m)/(512)` and first ball is pushed towards the second with kinetic energy `k_(0)`. [All collisions are elastic and head on]. The kinetic energy acquired by the last ball is `k_(10)`. In a separate experiment the `10^(th)` ball is pushed towards `9^(th)` ball with kinetic energy `k_(0)`. This time the kinetic energy acquired by `1^(st)` ball is `k_(1)`.
Compare `k_(10) and k_(1)`

Answer

(i) (a) `16 k_(0) (m^(2)M_(2))/((M+m)^(4))`
(b) `(##IJA_PHY_V01_C05_E01_067_A01##)`
(ii) `k_(10) = k_(1)`