An artillery piece of mass M₁$M_1$ fires a shell of mass M₂$M_2$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is :

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