Two balls of mass m each are connected by a weightless spring (figure) of force constant k and length of L and lie motionlessly on a smooth horizontal table. The third ball of mass m moves with speed

Question

Two balls of mass m each are connected by a weightless spring (figure) of force constant k and length of L and lie motionlessly on a smooth horizontal table. The third ball of mass m moves with speed of $v_{0}$ on the line connecting the centers of first two, and elastically collides with one of them. Assuming that time of impact of balls is very small in comparison to time of spring deformation :-

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Equal-mass elastic hit: the third ball stops and the struck ball moves at v 0 ​ - (B) true. The two spring balls oscillate about their COM with reduced mass μ = 2 m ​ . Amplitude: 2 1 ​ μ v 0 2 ​ = 2 1 ​ k A 2 ⇒ A = v 0 ​ 2 k m ​ ​ . L max ​ = L + A , L min ​ = L − A − ( A ) and (D) true. Answer: (A), (B), (D)

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