A body of mass 1 kg 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 of 15 ms^-1 each. What is the velocity of the heavier fragment?

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$10 \sqrt{2} m / s^{- 1}$

$5 \sqrt{2} m / s^{- 1}$

$5 \sqrt{3} m / s^{- 1}$

$10 \sqrt{3} m / s^{- 1}$

answer is D.

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Detailed Solution

Conservation of momentum during explosion yields
$\Rightarrow {\vec{p}}_{1} + {\vec{p}}_{2} + {\vec{p}}_{3} = 0 \Rightarrow {\vec{p}}_{3} = |{\vec{p}}_{1} + {\vec{p}}_{2}| \Rightarrow m_{3} v_{3} = |m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}|$
Since ${\vec{v}}_{1} ⊥ {\vec{v}}_{2} \Rightarrow v_{3} = \sqrt{\frac{m_{1}^{2} v_{1}^{2} + m_{2}^{2} v_{2}^{2}}{m_{3}}}$
$\Rightarrow v_{3} = \sqrt{\frac{{(m_{1})}^{2} v_{1}^{2}}{{m_{3}}^{2}} + \frac{{(m_{2})}^{2} v_{2}^{2}}{{m_{3}}^{2}}} = \sqrt{{(\frac{1}{3})}^{2} (15)^{2} + {(\frac{1}{3})}^{2} (15)^{2}}$