Question

A body of mass 1 kg initially at rest, explodes and breaks into three fragments of masses in the ration 1 : 1 : 3. The two pieces of equal mass fly off perpendicular to each other with a speed of 15 ms${}^{-1}$ each. What is the velocity of the heavier fragment?

• A. $10\sqrt{2}m{s}^{-1}$
• B. $5\sqrt{3}m{s}^{-1}$
• C. $10\sqrt{3}m{s}^{-1}$
• D. $5\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is D $5\sqrt{2}m{s}^{-1}$

Total mass of the body $M=1kg$

Ratio of the mass of the fragments $=1:1:3$

$\therefore$ $x+x+3x=1$ $⟹x=0.2$

Thus the mass of each fragment, $m_1=0.2kg$ $m_2=0.2kg$ $m_3=0.6kg$

Momentum of two equal pieces is $15$ $kgm/s$ each and fly off perpendicular to each other

$\therefore$ Momentum of the third piece $p_3=\sqrt{p_1^2+p_2^2}$

$p_3=\sqrt{{15}^2+{15}^2}=15\sqrt{2}$ $kg$ $m{s}^{-1}$

Thus velocity of third piece $v=\frac{p_3}{m_3}=\frac{15\sqrt{2}}{0.6}=5\sqrt{2}$ $m{s}^{-1}$