Question

A gun fires a bullet with velocity v. Mass of the bullet is m. The mass of the gun is M and it recoils with velocity V. If the kinetic energy of the bullet be $E_b$ and that gun be $E_g$, then

• A. $E_b=E_g$
• B. $E_b<E_g$
• C. $E_b>E_g$
• D. $E_b\ge E_g$

Answer 1

The correct option is C $E_b>E_g$

During gun fire linear momentum of the body will be conserved.

So $m_g.v_g=m_b.v_b$

And energy of the body given by $\frac{1}{2}m{v}^2$.

So when comparing kinetic energy of bullet and gun ww will get a factor $\frac{1}{2}mv.v$ where factor $\frac{1}{2}mv$ is same for both so the ratio will depend on $v$ of both the bodies.

As momentum is conserved and mass of bullet is less then mass of the gun this implies velocity of bullet will be more as compare to velocity of gun.

So $E_b>E_g$.

So option C is best possible.