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Question:

Statement - I: A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as f(1/2mv²), then f = (M/(M+m)). Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Statement I is true, Statement II is false.

Statement I is true, Statement II is true, Statement II is a correct explanation of Statement I.

Statement I is true, Statement II is true, Statement II is not a correct explanation of Statement I.

Statement I is false, Statement II is true

Solution:

Loss of energy is maximum when collision is inelastic as in an inelastic collision there will be maximum deformation. KE in COM frame is 1/2(Mm/(M+m))V²rel. KEi = 1/2(Mm/(M+m))V², KEf = 0 (.⋅ Vrel = 0). Hence loss in energy is 1/2(Mm/(M+m))V² ⇒ f = M/(M+m)