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Physics Question on laws of motion

A stationary body of mass m explodes into 3 parts of masses m in the ratio 1 : 3 : 3, its two fractions having equal masses moving at right angles to each other with a velocity of 15 ms−1ms^{-1}. What is the velocity of the third body

A

2 ms−1\sqrt{2}\,ms^{-1}

B

5 ms−15\,ms^{-1}

C

532 ms−15\sqrt{32}\,ms^{-1}

D

none of these

Answer

none of these

Explanation

Solution

Applying law of conservation of momentum, we get 2 p=p3\sqrt{2} \, p = p_3 i.e. 2×3m×15=m×υ\sqrt{2} \times 3m \times 15 = m \times \upsilon i.e. υ=452 m s−1\upsilon = 45\sqrt{2} \, m\, s^{-1}