Question

A bomb of mass $1kg$ initially at rest, explodes and breaks into three fragments of masses in the ratio $1:1:3$. The two pieces of equal mass fly off perpendicular to each other with a speed $15m/s$ each. The speed of heavier fragment is

• A. $5m/s$
• B. $15m/s$
• C. $45m/s$
• D. $5\sqrt{2}m/s$

Answer 1

Answer: (D)

$5\sqrt{2}m/s$

Masses are breaks in ratio $1:1:3$.

Let masses are $m_1=\frac{1}{5}$, $m_2=\frac{1}{5}$ and $m_3=\frac{3}{5}$,

Let mass $m_1$ and $m_2$ fly in direction $x$ and $y$ respectively. Let velocity of mass $m_3,V=V_x\hat{i}+V_y\hat{j}$

There is no external force, so momentum will be conserved.

Before the explosion, Linear momentum$=0$

After the explosion,

In direction $x$, Linear momentum$=m_1\times 15+m_3\times V_x=0$ $\Rightarrow V_x=-5$

In direction $y$, Linear momentum$=m_2\times 15+m_3\times V_y=0$ $\Rightarrow V_y=-5$

So speed of mass $m_3,V=\sqrt{(-5{)}^2+(-5{)}^2}=5\sqrt{2}$ $m/s$