Question

A rifle man, who together with his rifle has a mass of 100 kg, stands on a smooth surface and fires 10 shots horizontally. Each bullet has a mass 10 g and a muzzle velocity of 800 m s\(^{-1}\). The velocity which the rifle man attains after firing 10 shots is:

• A. \(8 \text{ m s}^{-1}\)
• B. \(0.8 \text{ m s}^{-1}\)
• C. \(0.08 \text{ m s}^{-1}\)
• D. \(-0.8 \text{ m s}^{-1}\)

Hint:

On a frictionless surface, total horizontal momentum is conserved. Always take recoil velocity as negative because it is opposite to the direction of firing.

Answer 1

The Correct Option is D

Step 1: Since the surface is smooth, there is no external horizontal force. Hence, linear momentum is conserved.
Step 2: Mass of one bullet \(= 10 \text{ g} = 0.01 \text{ kg}\) Number of bullets \(= 10\) Total mass of bullets fired: \[ m = 10 \times 0.01 = 0.1 \text{ kg} \] Velocity of bullets: \[ v = 800 \text{ m s}^{-1} \]
Step 3: Total momentum of bullets: \[ p = mv = 0.1 \times 800 = 80 \text{ kg m s}^{-1} \]
Step 4: Let the recoil velocity of the rifle man be \(V\). Mass of rifle man with rifle \(= 100 \text{ kg}\). By conservation of momentum: \[ 0 = 80 + 100V \] \[ 100V = -80 \] \[ V = -0.8 \text{ m s}^{-1} \]