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 m/s and 30 m/s, respectively, strike each other and stick together. The rise in temperature (in °C$^{\circ}C$), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material 31 cal/kg·°C$31 \text{ cal/kg}\cdot^{\circ}\text{C}$ and 1 cal = 4.2 J$1 \text{ cal} = 4.2 \text{ J}$)

Related Formula

Core Logic

By conservation of linear momentum (since no external horizontal force acts on the system):

Both the artillery and the shell acquire the exact same magnitude of momentum during firing.

Step 2: Kinetic Energy Ratio

The kinetic energy is related to momentum by KE = (p²)/(2m)$\text{KE} = \frac{p^2}{2m}$. Since p$p$ is identical for both bodies:

Therefore, the ratio of kinetic energy of the artillery (M₁$M_1$) to the shell (M₂$M_2$) is:

Chapter Mix

Class 11 Physics: Work, Energy And Power