WBJEE · Physics · Center of Mass Momentum and Collision

A shell of mass \(5 M\), acted upon by no external force and initially at rest, bursts into three fragments of masses \(M, 2 M\) and \(2 M\) respectively. The first two fragments move in opposite directions with velocities of magnitudes 2v and \(v\) respectively. The third fragment will

A move with a velocily \(v\) in a direction perpendicular To the other two
B move with a velocity \(2 v\) in the direction of velocity of the first fragment
C be at rest
D move with velocity \(v\) in the direction of velocity of the second fragment

Verified Solution

Answer & Solution

Correct Answer

(C) be at rest

Step-by-step Solution

Detailed explanation

Let the velocity of third fragment is \(v'\). Then by the conservation of linear momentum \[ \begin{aligned} & 5(0)=M \times 2 \mathrm{v}-2 M \times \mathrm{v}+2 \mathrm{M} \times \mathrm{v}^{\prime} \\ \Rightarrow \quad & \mathrm{v}^{\prime}=0 \end{aligned} \] i.e., the third…

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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