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A particle of mass $' m'$ moving with speed $' 2 v'$ and collides with a mass $' 2 m'$ moving with speed $' v'$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $' m',$ which move at angle $45^{°}$ with respect to the original direction. The speed of each of the moving particle will be

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$ν / (2 \sqrt{2})$

$\sqrt{2} ν$

$2 \sqrt{2} ν$

$ν \sqrt{2}$

answer is C.

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Detailed Solution

According to law of conservation of momentum,

$m (2 ν) + (2 m) ν = (m + m) ν^{'} \cos 45^{°}$

$4 m ν = 2 m ν^{'} \times \frac{1}{\sqrt{2}}$

$ν^{'} = 2 \sqrt{2} ν$

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