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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 $f (\frac{1}{2} m v^{2})$ then $f = \frac{m}{M + m} .$
Statement-II: Maximum energy loss occurs when the particles get stick together as a result of the collision.

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Statement –I is false, Statement – II is true.

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 true, Statement – II is false

answer is C.

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Detailed 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 $\frac{1}{2} (\frac{M m}{M + m}) V_{r e l}^{2}$

$K E_{i} = \frac{1}{2} (\frac{M m}{M + m}) V_{}^{2}, K E_{f} = 0 (∵ V_{r e l} = 0)$

Hence loss in energy is $\frac{1}{2} (\frac{M m}{M + m}) V_{}^{2} \Rightarrow f = \frac{M}{M + m}$

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