Conservation Of Momentum

Question

A stationary 5 kg gun fires a 0.02 kg bullet that leaves the muzzle at 250 m/s. Assuming no external horizontal force acts during firing, what is the recoil speed of the gun?

RankGuru · Accepted Answer

Since no external horizontal force acts on the gun-bullet system during firing, total linear momentum is conserved and must remain zero, as it was before firing. Let the bullet move forward with momentum $m_b v_b$ and the gun recoil backward with momentum $m_g v_g$. Conservation requires $m_g v_g = m_b v_b$, so $v_g = \frac{m_b v_b}{m_g} = \frac{0.02 	imes 250}{5} = \frac{5}{5} = 1.0	ext{ m/s}$. The 0.5 m/s value would result from doubling the gun's mass mistakenly. The 2.0 m/s value comes from using half the gun mass. The 5.0 m/s value equals the bullet's momentum without dividing by the gun's mass, which is dimensionally inconsistent for a speed. It is instructive to note that although total momentum stays zero, kinetic energy is not conserved here, because the chemical energy of the propellant is converted into the kinetic energy of both bodies, with the light bullet carrying the overwhelming share. This is the NCERT recoil illustration of momentum conservation, also the basis of rocket propulsion, where continuously expelled exhaust drives the rocket the opposite way. As a check, the heavy gun recoils far slower than the light bullet flies, exactly as the inverse mass ratio of 5 kg to 0.02 kg predicts.

Conservation Of Momentum

Select the correct option:

🔒 Solution Hidden from View

More laws of motion Practice Questions

In an isolated system with internal impulsive forces, which is conserved?

A block of weight 50 N rests on a horizontal floor while an external force of 20 N is applied on it ...

A pendulum hangs from the roof of a railway carriage that is accelerating horizontally, and the stri...

The linear momentum of a moving particle varies with time according to the relation p = 8 + 6t, wher...

A block placed on a rough inclined plane remains on the verge of sliding when the incline is tilted ...

A wooden block resting on a rough horizontal floor just begins to slide when a horizontal pull equal...

A small box slides down a smooth incline that makes an angle of 30 degrees with the horizontal surfa...

Two blocks of masses 3 kg and 2 kg are connected by a light string and pulled along a smooth horizon...

A person of mass 70 kg stands on a weighing scale inside a lift that accelerates upward at 2 m/s² wh...

A stone of mass 0.5 kg is whirled in a horizontal circle of radius 1 m at a constant speed of 4 m/s ...

A car negotiates a curved road of radius 100 m that is banked at an angle so that no friction is nee...

A football of mass 0.4 kg is kicked from rest and leaves the foot with a speed of 25 m/s after the f...

About This Question

Solution