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Question #43705

Difficulty: 8/10 | 🟢 Free

The Question

A system of mass $6m$ is initially at rest in the laboratory frame. It explodes into three fragments $A$ , $B$ , and $C$ of masses $m$ , $2m$ , and $3m$ respectively. The total kinetic energy released in the explosion is $Q$ . If fragment $C$ is observed to have a kinetic energy of $\frac{Q}{6}$ , what is the maximum possible kinetic energy of fragment $A$ in the laboratory frame?

Options

A.
$\frac{9 + 4\sqrt{2}}{18} Q$
B.
$\frac{5}{9} Q$
C.
$\frac{4}{9} Q$
D.
$\frac{9 - 4\sqrt{2}}{18} Q$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Energy Distribution in Beta Decay|Center of Mass (COM) Frame|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze a 3-body explosion (kinematically analogous to beta decay) by transforming between the Laboratory frame and the Center of Mass (COM) frame of the remaining two fragments.

The primary trap is assuming that the remaining energy ( $5Q/6$ ) is distributed between fragments A and B as if they were decaying from rest in the lab frame, which incorrectly yields $5Q/9$ (Option B).

Students often fail to recognize that the momentum carried away by fragment C forces the COM of A and B to recoil.

To correctly solve for the maximum kinetic energy, one must isolate the internal kinetic energy of the A-B system by subtracting the translational kinetic energy of their COM, find the velocity of A in this COM frame, and then vectorially add it to the COM velocity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Nuclei - Class 12
Concept	Energy Distribution in Beta Decay
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free