Question

A bomb at rest explodes into $3$ parts of same mass. The momentum of $2$ parts are $-2p\hat{i}$ and $p\hat{j}$ . The momentum of the third part will have a magnitude.

• A. $P$
• B. $\sqrt{3}P$
• C. $P\sqrt{5}$
• D. Zero

Answer 1

Answer: (C)

$\overset{ \rightarrow }{P}_{i}=\overset{ \rightarrow }{P}_{f}$
$0=-2P\hat{i}+P\hat{j}+\overset{ \rightarrow }{P}$
$\overset{ \rightarrow }{P}=-2P\hat{i}+P\hat{j}$
$\left|\right.P\left|\right.=\sqrt{4 P^{2} + P^{2}}=\sqrt{5}P$