Verified Solution • 2025–26 Session moderate

QJEEM13Ph8843: JEE Main 2013 Physics - Class 11 JEEM13Ph8843 Solution: This question has statement and statement . Of the four choices …

This question has statement I{\rm I} and statement I{\rm I} I{\rm I} . Of the four choices given after the statements, choose the one that best describes the two statements.

Statement - I{\rm I} : A point particle of mass mm moving with speed υ\upsilon collides with stationary point particle of mass M.M. If the maximum energy loss possible is given as f(12mv2)f\left( {{1 \over 2}m{v^2}} \right) , then f=(mM+m).f = \left( {{m \over {M + m}}} \right).

Statement - II{\rm II} : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Multiple Choice Options

  • A Statement - I{\rm I} is true, Statement - II{\rm II} is true; Statement - II{\rm II} is the correct explanation of Statement - I{\rm I} .
  • B Statement - I{\rm I} is true, Statement - II{\rm II} is true; Statement - II{\rm II} is not the correct explanation of Statement - I{\rm I} .
  • C Statement - I{\rm I} is true, Statement - II{\rm II} is false
  • D Statement - I{\rm I} is false, Statement - II{\rm II} true.

Step-by-Step Verified Solution

Initial energy = P22m{{{P^2}} \over {2m}} , where PP 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 = P22(m+M){{{P^2}} \over {2\left( {m + M} \right)}}

∴\therefore Maximum energy loss =P22m−P22(m+M)= {{{P^2}} \over {2m}} - {{{P^2}} \over {2\left( {m + M} \right)}} .

[\left[ \right. As K.E.=P22m=12mv2  ]\left. {K.E. = {{{P^2}} \over {2m}} = {1 \over 2}m{v^2}\,\,} \right]

=P22m[M(m+M)]=12mv2{Mm+M}= {{{P^2}} \over {2m}}\left[ {{M \over {\left( {m + M} \right)}}} \right] = {1 \over 2}m{v^2}\left\{ {{M \over {m + M}}} \right\}

∴\therefore f=(Mm+M)f = \left( {{M \over {m + M}}} \right)

So statement II is wrong.

Statement II{\rm I}{\rm 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 I{\rm I} I{\rm I} is correct.

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