Question

A shell of mass $200 \,gm$ is ejected from a gun of mass $4\, kg $ by an explosion that generates $1.05 \,kJ$ of energy. The initial velocity of the shell is

• A. 40 ms$^{-1}$
• B. 120 ms$^{-1}$
• C. 100 ms$^{-1}$
• D. 80 ms$^{-1}$

Answer 1

Answer: (C)

$m v=M v^{\prime} \Rightarrow v^{\prime}=\left(\frac{m}{M}\right) v$
Total K.E. of the bullet and gun
$=\frac{1}{2} m v^{2}+\frac{1}{2} M v^{\prime 2}$
Total K.E $=\frac{1}{2} m v^{2}+\frac{1}{2} M \cdot \frac{m^{2}}{M^{2}} v^{2}$
Total K.E. $=\frac{1}{2} m v^{2}\left\{1+\frac{m}{M}\right\}$
$=\left\{\frac{1}{2} \times 0.2\right\}\left\{1+\frac{0.2}{4}\right\} v^{2}$
$=1.05 \times 1000\, J$
$\Rightarrow v^{2}=\frac{4 \times 1.05 \times 1000}{0.1 \times 4.2}=100^{2} ;$
$\therefore v=100 \,ms ^{-1}$