Question

A gun of mass $50$ $kg$ fires a bullet of mass $0.5$ $kg$ with velocity of $200m{s}^{-1}$. If the gun moves through $1$ $m$ back before coming to rest, the frictional force on the gun is:

• A. 50 N
• B. 100 N
• C. 200 N
• D. Zero

Answer 1

The correct option is B 100 N

From the momentum conservation, we have
Initial momentum $=$ final momentum.
Therefore, if V is the velocity of gun just after firing then
$0=50V+0.5\times 200$
$V=-2m/s$ (-ve sign indicates direction of gun is opposite to that of bullet)

Now, since the final velocity of gun is zero,
$0-(-2{)}^2=2a\times 1$
$a=-2m/s^2$ (-ve sign indicates deceleration)

Therefore frictional force is equal to force with which gun is moving backward
$F=2\times 50=100N$