This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
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)/(2)mv^(2))"then "f=((m)/(M+m)).`
Statement - II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Options

A. Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Stateme
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

D

Explanation

Loss of energy is maximum when collision is inelastic as in an inelastic collision there will be maximum deformation.
`K.E_(i) = 1/2 mv^2 , " " mv = (m + M)v_f implies v_f = ((m)/(m + M))v`
`K.E_(f) - K.E_(i) = 1/2(M + m)v_f^2 - 1/2 mv^2 = 1/2 mv^2 ((M)/(m + M))`
Hence loss in energy is `1/2((Mm)/(M + m)) v^2 implies f = (M)/(M + m)`