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

Question

A bomb at rest explodes into three parts of equal mass. If the momentum of two parts are $-2 p \hat{\mathbf{i}}$ and $p \hat{\mathbf{j}}$, find the magnitude of momentum of the third part., $p$, $\sqrt{3} p$, $\sqrt{5} p$, 0

MARKS App · Accepted Answer

If $p^{\prime} \hat{\mathbf{n}}$ be the momentum of third parts, then according to conservation of linear momentum. Total moment before explosion $=$ Total momentum after explosion $\begin{array}{lll} & \Rightarrow 0 =-2 p \hat{\mathbf{i}}+p \hat{\mathbf{j}}+p^{\prime} \hat{\mathbf{n}} \ & \Rightarrow p^{\prime} \hat{\mathbf{n}} =2 p \hat{\mathbf{i}}-p \hat{\mathbf{j}} \ & \therefore \text {Magnitude of } p^{\prime} \hat{\mathbf{n}}=p^{\prime} \ & =\sqrt{(2 p)^2+(-p)^2}=\sqrt{5 p^2}=\sqrt{5 p} \end{array}$

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