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

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

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.