A gun of mass 5 kg fires a bullet of mass 10⁻² kg with a speed of 500 m s⁻¹. The ratio of the kinetic energy of the bullet to that of the gun is N × 10³. Find N.
Physics · Mixed Chapter
JEE Main Practice

Question

A gun of mass 5 kg fires a bullet of mass 10⁻² kg with a speed of 500 m s⁻¹. The ratio of the kinetic energy of the bullet to that of the gun is N × 10³. Find N.

G1 Physics · Accepted Answer

Step 1: Initial momentum is zero; gun and bullet recoil with equal and opposite momentum magnitude p. Step 2: Kinetic energy at fixed momentum: K = p²/(2m). Step 3: Therefore Kbullet/Kgun = Mgun/mbullet = 5/(10⁻²) = 500. Step 4: 500 = 0.5 × 10³. Final answer: N = 0.5.