A stationary particle explodes into three fragments. Momentum of two fragments are ${\vec{P}}_{1} = (4 \hat{i} + 3 \hat{j}) kg - m / s and {\vec{P}}_{2} = (- \hat{i} + \hat{j}) kg - m / s .$ Then magnitude of momentum of the third particle is ______.

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$4 \sqrt{3} kg - m / s$

$6 \sqrt{5} kg - m / s$

$3 \sqrt{2} kg - m / s$

$5 kg - m / s$

answer is B.

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Detailed Solution

$\begin{array}{l} {\vec{P}}_{1} + {\vec{P}}_{2} + {\vec{P}}_{3} = 0 \Rightarrow {\vec{P}}_{3} = - (3 \hat{i} + 4 \hat{j}) kg - m / s \\ ∴ P_{3} = \sqrt{3^{2} + 4^{2}} kg - ms = 5 kg - m / s \end{array}$

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