Two small smooth spheres $$\(A\)$$ and $$\(B\)$$, of equal radii and of masses $$\(\mathrm{km} \mathrm{kg}\)$$ and $$\(m \mathrm{~kg}\)$$ respectively, where $$\(k> 1\)$$, are free to move on a smooth horizontal plane. $$\(A\)$$ is moving towards $$\(B\)$$ with speed $$\(6 \mathrm{~m} \mathrm{~s}^{-1}\)$$ and $$\(B\)$$ is moving towards $$\(A\)$$ with speed $$\(2 \mathrm{~m} \mathrm{~s}^{-1}\)$$. After the collision $$\(A\)$$ and $$\(B\)$$ coalesce and move with speed $$\(4 \mathrm{~m} \mathrm{~s}^{-1}\)$$. Find, in terms of $$\(m\)$$, the loss of kinetic energy due to the collision. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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