This question has statement 1 and statement 2 . Of the four choic… - Vidyadip

MCQ

This question has statement $1$ and statement $2$ . Of the four choices given after the statements, choose the one that best describes the two statements.
Statement $- 1$: A point particle of mass m moving with speed $u$ 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 $-2$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A
Statement $-1$ is true, Statement $-2$ is true ;

Statement $-2$ is the correct explanation of Statement $-1$
B
Statement $-1$ is true, Statement $-2$ is true ;

Statement $-2$ is not the correct explanation of Statement $-1$
✓
Statement $-1$ is false, Statement $-2$ is true
D
Statement $-1$ is true, Statement $-2$ is false

✓

Answer

Correct option: C.

Statement $-1$ is false, Statement $-2$ is true

c
Maximum energy loss $=\frac{{{P^2}}}{{2m}} - \frac{{{P^2}}}{{2\left( {m + M} \right)}}$

$\left[ {\because \,K.E. = \frac{{{P^2}}}{{2m}} = \frac{1}{2}m{v^2}} \right]$

$ = \frac{{2{P^2}}}{{2m}}\left[ {\frac{M}{{\left( {m + M} \right)}}} \right] = \frac{1}{2}m{v^2}\left\{ {\frac{M}{{m + M}}} \right\}$

Statement II is a case of perfectly inelastic collision.By comparing the equation given in statement I with abpve equation, we get

$f = \left( {\frac{M}{{m + M}}} \right)\,instead\,of\,\left( {\frac{m}{{M + m}}} \right)$

Hence statement $I$ is wrong and statement $II$ is correct.

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