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(C) According to the law of conservation of linear momentum,the total momentum of the system before and after the explosion must be zero,as the bomb w

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$\sqrt{5} p$

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(C) According to the law of conservation of linear momentum,the total momentum of the system before and after the explosion must be zero,as the bomb was initially at rest.Let $\vec{p}_3$ be the momentum of the third part.$\vec{p}_1 + \vec{p}_2 + \vec{p}_3 = 0$Given $\vec{p}_1 = -2p \hat{i}$ and $\vec{p}_2 = p \hat{j}$.$-2p \hat{i} + p \hat{j} + \vec{p}_3 = 0$$\vec{p}_3 = 2p \hat{i} - p \hat{j}$The magnitude of the momentum of the third part is given by:$|\vec{p}_3| = \sqrt{(2p)^2 + (-p)^2}$$|\vec{p}_3| = \sqrt{4p^2 + p^2}$$|\vec{p}_3| = \sqrt{5p^2} = \sqrt{5} p$

$A$ bomb at rest explodes into three parts of equal mass. If the momentum of two parts are $-2 p \hat{i}$ and $p \hat{j}$,find the magnitude of momentum of the third part.

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