consider a stiff plate on anything through which nothin can penetrate

if i fire a bullet in front of it the bullet hits it with some force, then the plate should also exert equal force on it and the bullet should go back into the gun,my question is, why doesn't it happen so?

Hi Amit

The Newtons third law is valid here too, the stiff plate applies equal and opposite force on the bullet. But this is not an ideal situation, the energy contained in the bullet does not remain the same. This is because of the friction losses , conversion of the energy into heat and sound energy, due to which the bullet cannot reach back into the gun.

If there were no friction or any other kind of losses then it would have been possible for the bullet to go back in the gun. Moreover there are also no plate that can be  perfectly stiff. It too undergoes slight deformation. What you are talking about are ideal conditions and not what is real sitution.