Momentum and CollisionHard

Question

A particle moving with kinetic energy  = 3J makes an elastic head - on collision with a stationary particle which has twice its mass. During the impact,

Options

A.the minimum kinetic energy of the system is 1J
B.the maximum elastic potential energy of the system is 2J.
C.momentum and total energy are conserved at evergy instant.
D.the ratio of kinetic energy to potential energy of the system first decreases and then increase

Solution

At the time collision both particles have common velocity and hence the system has minimum kinetic energy.
KEinitial  = mu2 = 3J
KEcollision  = (3m)v2 = (3m) = 1J
PEcollision  = (3 - 1) = 2J
Total energy remains constant and hence KE of system first decrease & then increases.

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