Question 216: Centre of Mass and Rotational Motion

Question

This question has statement ${\rm I}$ and statement ${\rm I}$${\rm I}$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - ${\rm I}$:
A point particle of mass $m$ moving with speed $\upsilon $ collides with stationary point particle of mass $M.$ If the maximum energy loss possible is given as $f\left( {{1 \over 2}m{v^2}} \right)$, then $f = \left( {{m \over {M + m}}} \right).$
Statement - ${\rm II}$:
Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Accepted Answer

Initial energy =  ${{{P^2}} \over {2m}}$, where $P$ is the momentum and m is the mass of the moving particle.
Loss of energy is maximum when collision is inelastic means when the particles get stuck together as a result of the collision.
So after collision energy = ${{{P^2}} \over {2\left( {m + M} ight)}}$
$	herefore$ Maximum energy loss $ = {{{P^2}} \over {2m}} - {{{P^2}} \over {2\left( {m + M} ight)}}$.
$\left[  ight.$ As $\left. {K.E. = {{{P^2}} \over {2m}} = {1 \over 2}m{v^2}\,\,} ight]$
$ = {{{P^2}} \over {2m}}\left[ {{M \over {\left( {m + M} ight)}}} ight] = {1 \over 2}m{v^2}\left\{ {{M \over {m + M}}} ight\}$
$	herefore$ $f = \left( {{M \over {m + M}}} ight)$
So statement $I$ is wrong.
Statement ${m I}{m I}$ says "Maximum energy loss occurs when the particles get stuck together as a result of the collision." This is a case of perfectly inelastic collision.
Hence statement ${m I}$${m I}$ is correct.

Answer

Statement - ${\rm I}$ is true, Statement - ${\rm II}$ is true; Statement - ${\rm II}$ is the correct explanation of Statement - ${\rm I}$.

Answer

Statement - ${\rm I}$ is true, Statement - ${\rm II}$ is true; Statement - ${\rm II}$ is not the correct explanation of Statement - ${\rm I}$.

Answer

Statement - ${\rm I}$ is true, Statement - ${\rm II}$ is false

Answer

Statement - ${\rm I}$ is false, Statement - ${\rm II}$ true.

Centre of Mass and Rotational Motion

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