A body of mass 5 kg explodes at rest into three fragments with masses in the rat

Question

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be

Options:

A . 11.5 m/s

B . 14.0 m/s

C . 7.0 m/s

D . 9.89 m/s

Answer: Option D
:
D

A Body Of Mass 5 Kg Explodes At Rest Into Three Fragments Wi...

P_{x} = m \times v_{x} = 1 \times 21 = 21 k g m / s

P_{y} = m \times v_{y} = 1 \times 21 = 21 k g m / s

∴

Resultant =

\sqrt{P_{x}^{2} + P_{y}^{2}} = 21 \sqrt{2} k g m / s

The momentum of heavier fragment should be numerically equal to resultant of

{\to P}_{x}

and

{\to P}_{y}

3 \times v = \sqrt{P_{x}^{2} + P_{y}^{2}} = 21 \sqrt{2} ∴ v = 7 \sqrt{2} = 9.89 m / s

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