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A body of mass m at rest explodes into 3 partrs, having masses in ratio 1:1:3. If two parts having equal masses move at right angles to each other with 10 m/s each , the velocity of third will be

\[(a)\;\sqrt 2 \;m/s \quad (b)\;5 \sqrt 2\;m/s \quad (c)\;5\;m/s \quad (d)\;10 \sqrt 2\;m/s\]
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1 Answer

Let the mass of each part be $\large\frac{m}{5},\frac{m}{5},\frac{3m}{5}$
Momentum of each part flying at right angle will be same and at $45^{\circ}$ with the third part.
$\large\frac{m}{5}$$ \times 15 \cos 45 +\large\frac{m}{5}$$ \times 15 \cos 45=\large\frac{3m}{5}$$v$
$\large\frac{15}{\sqrt 2}+\frac{15}{\sqrt 2}$$=3v$
$v= \large\frac{10}{\sqrt 2}$
$\quad=5 \sqrt 2\;m/s$
Hence b is the correct answer.
answered Jul 22, 2013 by meena.p
edited Jun 5, 2014 by lmohan717

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