Question

A bomb at rest explodes into $3$ parts on same mass. The momentum of two parts is $-3P\hat{i}$ and $2P\hat{j}$ respectively. The magnitude of the momentum of the third part is.

• A. $P$
• B. $\sqrt{5}P$
• C. $\sqrt{11}P$
• D. $\sqrt{13}P$

Answer 1

The correct option is D $\sqrt{13}P$

Given that:- $\overrightarrow{P_1}=-3P\hat{i}$ and $\overrightarrow{P_2}=2P\hat{j}$

And $m_1=m_2=m_3=\frac{m}{3}$

And $\overrightarrow{P_{initial}}=0$

Let momentum of third part be $\overrightarrow{P_3}$

Applying principle of conservation of linear momentum:-

$\overrightarrow{P_{final}}=\overrightarrow{P_{initial}}$

$⟹\frac{m}{3}\overrightarrow{P_1}+\frac{m}{3}\overrightarrow{P_2}+\frac{m}{3}\overrightarrow{P_3}=0$

$⟹\overrightarrow{P_1}+\overrightarrow{P_2}+\overrightarrow{P_3}=0$

$⟹-3P\hat{i}+2P\hat{j}+\overrightarrow{P_3}=0$

$⟹\overrightarrow{P_3}=3P\hat{i}-2P\hat{j}$

$⟹P_3=\sqrt{13}P$

Hence, answer is option-(D).