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

G1 Physics · Accepted Answer

By conservation of momentum, the magnitudes of momenta of the artillery and shell are equal. KE = p²/(2M) For the same p, KE ∝ 1/M. Therefore, K E a r t i l l e r y E_artillery E a ​ r t i l l er y / K E s h e l l E_shell E s ​ h e l l = M₂/M₁