A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly ea...

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A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly each after with a velocity of \( 12 \mathrm{~m} / \mathrm{s} \), then the velocity of the third part which has 3 times mass of each part is [Similar CBSE PMT 1991;
AMU (Engg.) 1991; UPSEAT 2001; EAMCET 2009]
(a) \( 4 \sqrt{2} \mathrm{~m} / \mathrm{s} \) at an angle of \( 45^{\circ} \) from each body
(b) \( 24 \sqrt{2} \mathrm{~m} / \mathrm{s} \) at an angle of \( 135^{\circ} \) from each body
(c) \( 6 \sqrt{2} \mathrm{~m} / \mathrm{s} \) at \( 135^{\circ} \) from each body
(d) \( 4 \sqrt{2} \mathrm{~m} / \mathrm{s} \) at \( 135^{\circ} \) from each body
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