Question

A bullet of mass .01 kg is fired from a gun of mass 5kg if the initial velocity of the bullet is 250 metre per second and the gun recoils at a velocity?

Answer 1

Given:

Mass of Bullet, m= 0.01 kg

Mass of Gun, M= 5 kg

Initial velocity of Bullet, v= 250 m/s

To Find:

Recoil velocity of Gun

Solution:

Let the recoil velocity of gun be V

We know that,

• Momentum= Mass×Velocity

• According to Law of conservation of momentum, for a system, in the absence of an external force

$\sf{Initial\:Momentum\:of\:System=Final\:Momentum\:of\:System}$

i.e.  $\mathrm{P_{i}=P_{f}}$ or $\mathrm{m_{1}v_{1}=m_{2}v_{2}}$

Now, on applying law of conservation of momentum on given system of bullet and gun, we get

$\longrightarrow\mathrm{P_{i}=P_{f}}$

But here initial momentum of system is 0

Therefore, $\mathrm{P_{i}=0}$

So,

$\longrightarrow\mathrm{0=P_{f}}$

$\longrightarrow\mathrm{P_{f}=0}$

$\longrightarrow\mathrm{MV+mv=0}$

$\longrightarrow\mathrm{(5)V+(0.01)(250)=0}$

$\longrightarrow\mathrm{5V+2.5=0}$

$\longrightarrow\mathrm{5V=-2.5}$

$\longrightarrow\mathrm{V=\dfrac{-2.5}{5}}$

$\longrightarrow\mathrm{\green{V=-0.5\:m/s}}$

Hence, recoil velocity of gun is -0.5 m/s.