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.

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(C) Statement \(-1\) is false, Statement \(-2\) is true

Detailed explanation

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 12.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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