Why the recoil velocity of a gun is much less than the velocity of the bullet .explain by using the principle of conservation of linear momentum ?

The principle of conservation of linear momentum states that the total momentum of a system remains constant if no external forces are acting on it. In the case of a gun firing a bullet, the initial momentum of the system (gun and bullet) is zero because they are at rest. When the gun is fired, the bullet gains momentum in one direction, causing the gun to gain an equal but opposite momentum in the other direction.

Since momentum is mass times velocity, the momentum of the bullet is much greater than the momentum of the gun due to the bullet's higher velocity. This is because the bullet has much less mass than the gun, so even though the gun and bullet have equal and opposite momenta, the bullet's higher velocity results in a much larger momentum.

Therefore, the recoil velocity of the gun is much less than the velocity of the bullet because the gun has a much larger mass than the bullet. This is a direct result of the conservation of linear momentum, where the total momentum of the system remains constant and is distributed between the gun and the bullet in opposite directions.