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An object, initially at rest, explodes in three fragments. The momentum of two pieces are $- 3 p i a n d - 4 p j$ where p is a positive number. The momentum of the third piece
(i) will have magnitude $5 p$
(ii) will make an angle $\tan^{- 1} (4 / 3)$ with the x-axis
(iii) will make an angle $\tan^{- 1} (34)$ with the x-axis
(iv) will have magnitude $7 p$

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(i), (iii)

(i), (ii)

(ii), (iv)

(iii), (iv)

answer is B.

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Detailed Solution

$= (- 3 p + p_{x}) \hat{i} + (- 4 p + p_{y}) j - 3 p + p_{z} = 0 \Rightarrow p_{z} = 3 p - 4 p + p_{y} = 0 \Rightarrow p_{y} = 4 p$

\end{aligned}

The momentum of the third piece

$| p | = \sqrt{(3 p)^{2} + (4 p)^{2}} = 5 p \tan θ = \frac{4 p}{3 p} \Rightarrow θ = \tan^{- 1} (\frac{4}{3})$

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