Question

If the Mass of gun $=2kg$
Mass of bullet $=20gm$
Velocity of bullet after firing $=200m/s$

Then the Velocity of gun after firing will be

Answer 1

Given that,

Mass of gun $M=2kg$

Mass of bullet$m=20g=0.02kg$

Initial velocity of bullet $v_2=200m/s$

Initial velocity of gun $v_1=0$

Now, total initial momentum of gun and bullet

$(m_1+m_2)v=0$

Now, total momentum of gun and bullet after firing

$m_1{v}_1+m_2{v}_2=2v_1+0.02\times 200$

$m_1{v}_1+m_2{v}_2=2v_1+4$

$0=2v_1+4$

Now, Law of conservation of linear momentum

Total momentum after firing = total momentum before firing

$2v_1+4=0$

$v_1=-2m/s$

negative sign represent opposite direction of bullet

Hence, the velocity of the gun after firing $v_1=-2m/s$