Question

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

• 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 $E_b>E_g$

Linear momentum is conserb

$mv=MV$

$V=\frac{m}{M}v$

$E_b=\frac{1}{2}m{V}^2$ and $E_g=\frac{1}{2}M{V}^2=\frac{1}{2}\frac{m^2}{M}{v}^2$

Here $\frac{m}{M}<1$

therefore $E_g<E_b$ Option - C