Question

A gun of mass 1000 kg fires a projectile of mass 1 kg with a horizontal velocity of 100 m/s. The velocity of recoil of the gun in the horizontal direction is

• A. 5 m/s
• B. 0.1 m/s
• C. 15 m/s
• D. 20 m/s

Hint:

In recoil problems, always apply conservation of momentum assuming the system is isolated and starts at rest.

Answer 1

The Correct Option is B

Using the principle of conservation of momentum, the total momentum before and after firing should remain zero (assuming the system was initially at rest).
Let \( M = 1000 \, \text{kg} \) (mass of gun), \( m = 1 \, \text{kg} \) (mass of projectile), \( v = 100 \, \text{m/s} \) (velocity of projectile), and \( V \) be the recoil velocity of the gun.
\[ \text{Initial momentum} = 0 \] \[ \text{Final momentum} = M(-V) + m(v) = 0 \Rightarrow -1000V + 1 \times 100 = 0 \] \[ 1000V = 100 \Rightarrow V = \frac{100}{1000} = 0.
1 \, \text{m/s} \]