Bullet-Gun System Kinetic Energy Ratio – Rankers Physics

Collision: Practice Problem & Solution

Assertion (A): In case of bullet fired from a gun, the ratio of kinetic energy of gun and bullet is equal to ratio of masses of bullet and gun. Reason (R): In firing of bullet, linear momentum of system is conserved.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Collision. Understanding the underlying formula is key to arriving at the correct answer below:

Reason (R): For the bullet-gun system, the forces causing the bullet to fire are internal. Thus, linear momentum of the system is conserved. So, (R) is true.

Assertion (A): Let (m\) and (M\) be masses of bullet and gun, (v\) and (V\) their velocities. By momentum conservation, (mv = MV\). The ratio of kinetic energies is \( \frac{K_g}{K_b} = \frac{\frac{1}{2}MV^2}{\frac{1}{2}mv^2} = \frac{M(mv/M)^2}{mv^2} = \frac{m}{M}\). So, (A) is true.

(R) correctly explains (A) as the kinetic energy ratio is derived directly from momentum conservation. Option (1) is correct.

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