# A gun of mass M fires a bullet of mass m with maximum speed v. Given that m < M .The kinetic energy of the gun will be

Q: A gun of mass M fires a bullet of mass m with maximum speed v. Given that m < M .The kinetic energy of the gun will be

(a) 1/2 mv2

(b) 1/2 Mv2

(c) more than 1/2 mv2

(d) less than 1/2 mv2

Ans: (d)
Sol: $\displaystyle 0 = m \vec{v} + M \vec{v_1}$

$v_1 = – \frac{m}{M} v$

Kinetic energy of the gun will be

$K.E = \frac{1}{2} M v_1^2$

$K.E = \frac{1}{2} M (\frac{m}{M} v)^2$

$K.E = \frac{1}{2 M} m^2 v^2$

$K.E = \frac{m}{M} ( \frac{1}{2 } m v^2 ) < \frac{1}{2 } m v^2$