A shell of mass $200 \mathrm{~g}$ 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

Question

Aicharya · Accepted Answer

Key Idea: In the given problem conservation of linear momentum and energy hold good.
Conservation of momentum yields.
$\begin{aligned}
& m_1 v_1+m_2 y_2=0 \\
& \text{or } 4 y_1+0.2 y_2=0
\end{aligned}$
Conservation of energy yields
$\begin{array}{l}
& \frac{1}{2} m_1 y_1^2+\frac{1}{2} m_2 y_2^2=1050 \\
& \text {or } \frac{1}{2} \times 4 y_1^2+\frac{1}{2} \times 0.2 \times y_2^2=1050 \\
& \text {or } 2 v_1^2+0.1 v_2^2=1050
\end{array}$
Solving Eqs. (i) and (ii), we have
$v_1=100 \mathrm{~m} / \mathrm{s}$ .

A shell of mass $200 \mathrm{~g}$ is ejected from a gun of mass $4 \mathrm{~kg}$ by an explosion that…

Solution