Question

a bullet of mass 20g is fired from a gun of mass 8kg with a velocity of 400m/s find out the recoil velocity of the gun .

Answer 1

1m/s
V = (m/M)v
V =velocity of gun
v = velocity of bullet
m = mass of bullet
M =mass of gum

Answer 2

Answer:

The recoil velocity of the gun is 1m/s.

Explanation:

Given mass of the bullet, $m_b= 20g= 0.02 kg$

mass of the gun, $m_g= 8 kg$

Bullet is fired with a  velocity, $v_b= 400 m/s$

Initially, the rifle and bullet is at rest, hence its initial velocity, u = 0

Let the recoil velocity of the gun be $v_g$

Applying the conservation of linear momentum,

Initial momentum  = Final momentum

$(m_b+m_g)u=m_bv_b+m_gv_g$

$\implies 0=0.02\times 400+8\times v_g$

$\implies v_g=-\frac{2\times 4}{8} =-1m/s$

Negative sign gives the direction of recoil velocity in backward direction.

Therefore, the magnitude of the recoil velocity of the gun is 1m/s.