A bomb at rest explodes into 3 parts of same mass. The momentum of two parts is -3pi^ and 2pj^ respectivley. The magnitude of momentum of the third part is

MHT CET · Physics · Center of Mass Momentum and Collision

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

A $p$
B $\sqrt{5} p$
C $\sqrt{11} p$
D $\sqrt{13} p$

Verified Solution

Answer & Solution

Correct Answer

(D) $\sqrt{13} p$

Step-by-step Solution

Detailed explanation

As initial momentum is zero, final will be also zero

$\therefore p_3=\sqrt{9 p^2+4 p^2}=\sqrt{13} p.$

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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