Question

A shell of mass $200gm$ is ejected from a gun of mass $4kg$ by an explosion that generates $1.05kJ$ 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)

$mv=M{v}^{\prime }\Rightarrow v^{\prime }=\left(\frac{m}{M}\right)v$
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. $=\frac{1}{2}m{v}^2\left\{1+\frac{m}{M}\right\}$
$=\left\{\frac{1}{2}\times 0.2\right\}\left\{1+\frac{0.2}{4}\right\}{v}^2$
$=1.05\times 1000J$
$\Rightarrow v^2=\frac{4\times 1.05\times 1000}{0.1\times 4.2}=100^2;$
$\therefore v=100m{s}^{-1}$