A particle of mass m , kinetic energy K and momentum p collides head on elastically with another particle of mass 2 m at rest. After collision : List - I List - II (I) Momentum of first particle (P) 3

Question

A particle of mass m , kinetic energy K and momentum p collides head on elastically with another particle of mass 2 m at rest. After collision : List - I List - II (I) Momentum of first particle (P) 3 4 p ​ (II) Momentum of second particle (Q) 3 − p ​ (III) Kinetic energy of first particle (R) 9 8 K ​ (IV) Kinetic energy of second particle (S) 9 K ​ (T) 9 4 K ​

TestHub · Accepted Answer

Elastic head-on: v 1 ′ ​ = m + 2 m m − 2 m ​ u = − 3 u ​ v 2 ′ ​ = 3 m 2 m ​ u = 3 2 u ​ (I) p 1 ′ ​ = m ( − u /3 ) = − p /3 → Q. (II) p 2 ′ ​ = 2 m ( 2 u /3 ) = 4 p /3 → P. (III) K E 1 ′ ​ = 2 1 ​ m ( u /3 ) 2 = K /9 → S. (IV) K E 2 ′ ​ = 2 1 ​ ( 2 m ) ( 2 u /3 ) 2 = 9 4 ​ m u 2 = 9 8 K ​ → R. Option (A). (Printed option B repeats S for I and III, so it cannot be correct.)

List - I	List - II
(I) Momentum of first particle	(P) $\frac{4 p}{3}$
(II) Momentum of second particle	(Q) $\frac{- p}{3}$
(III) Kinetic energy of first particle	(R) $\frac{8 K}{9}$
(IV) Kinetic energy of second particle	(S) $\frac{K}{9}$
	(T) $\frac{4 K}{9}$

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