Question

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

• A. Statement I is true, Statement II is true, Statement II is not a correct explanation of Statement I.
• B. Statement I is true, Statement II is false.
• C. Statement I is false, Statement II is true
• D. Statement I is true, Statement II is true, Statement II is a correct explanation of Statement I.

Answer 1

The correct option is C Statement I is false, Statement II is true

Loss of energy is maximum when collision is inelastic as in an inelastic collision there will be maximum deformation.

$KE$ in COM frame is $\frac{1}{2}\left(\frac{Mm}{M+m}\right)V_{rel}^2$

$K{E}_i=\frac{1}{2}\left(\frac{Mm}{M+m}\right)V^2,K{E}_f=0(.\cdot V_{rel}=0)$

Hence loss in energy is $\frac{1}{2}\left(\frac{Mm}{M+m}\right)V^2$

$\Rightarrow f=\frac{M}{M+m}$