A shell of mass $200 \mathrm{gm}$ is ejected from a gun of mass $4 \mathrm{~kg}$ by an explosion that…
A shell of mass $200 \mathrm{gm}$ is ejected from a gun of mass $4 \mathrm{~kg}$ by an explosion that generates $1.05 \mathrm{~kJ}$ of energy. The initial velocity of the shell is
$120 \mathrm{~ms}^{-1}$
$100 \mathrm{~ms}^{-1}$
$80 \mathrm{~ms}^{-1}$
$40 \mathrm{~ms}^{-1}$
Solution
Let the initial velocity of the shell be $\mathrm{v}$, then velocity of gun is $\left(\frac{0.2 v}{4}\right)$. (from conservation of linear momentum)
Now $1.05 \times 10^3=\frac{1}{2}(0.2) v^2+\frac{1}{2}(4)\left(\frac{0.2 v}{4}\right)^2 \Rightarrow v=100 \mathrm{~m} / \mathrm{s}$
.