JEE Main 2026 — Center of Mass Momentum and Collision Question with Solution

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of $10\mathrm{m}/\mathrm{s}$ and $30\mathrm{m}/\mathrm{s}$, respectively, strike each other and stick together. The rise in temperature (in ${}^{\circ }\mathrm{C}$), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material $31\mathrm{cal}/\mathrm{kg}.{}^{\circ }\mathrm{C}$ and $1\mathrm{cal}=4.2\mathrm{J}$)