A shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. If one of those parts having…
A shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. If one of those parts having mass $m / 6$ remains stationary, find the velocity of the other part.
$\frac{6 v}{5}$
$2 v$
$\frac{3 v}{4}$
$\frac{4 v}{3}$
Solution
Given that, mass of shell $=m$
Mass of lst part, $m_1=\frac{m}{6}$
Then, mass of 2nd part, $m_2=m-\frac{m}{6}=\frac{5 m}{6}$
Velocity of lst part, $v_1=0$
Velocity of shell $=v$
Let velocity of 2nd part $=v_2$
By using law of conservation of linear momentum,
Initial linear momentum $=$ final linear momentum.
$m v=m_1 v_1+m_2 v_2$
Substituting the values, we get
$m v=\frac{m}{6} \times 0+\frac{5 m}{6} \times v_2$
$\Rightarrow \quad v_2=\frac{6}{5} v$
Hence, the velocity of 2 nd part is $\frac{6}{5} v$ in the same direction as that of shell.