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Question #42048

Difficulty: 8/10 | 🟢 Free

The Question

A parent nucleus $A$ of mass $4m$ , initially at rest in the laboratory frame, undergoes a spontaneous decay into a nucleus $B$ of mass $3m$ and a particle $C$ of mass $m$ , releasing a total kinetic energy $Q_1 = 6Q$ . Subsequently, nucleus $B$ decays in flight into a nucleus $D$ of mass $2m$ and a particle $E$ of mass $m$ , releasing a total kinetic energy $Q_2 = 3Q$ . Assuming all motion is one-dimensional and non-relativistic, what is the maximum possible velocity of nucleus $D$ in the laboratory frame?

Options

A.
$2\sqrt{\frac{Q}{m}}$
B.
$\sqrt{\frac{2Q}{m}}$
C.
$\sqrt{\frac{Q}{m}}$
D.
$\frac{3}{2}\sqrt{\frac{Q}{m}}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Relative Velocity in 1D|Reduced Mass Effect|Successive Decay Equilibrium

Why This Question Is Tricky

Common Mistakes

This question tests the application of Galilean velocity transformations in successive nuclear decays.

A common trap is treating the second decay entirely in the laboratory frame, ignoring that the Q-value energy $Q_2$ is released in the center-of-mass frame of the decaying parent $B$ .

Students often incorrectly add the kinetic energies directly in the lab frame (yielding option B) or fail to account for the initial momentum of $B$ entirely (yielding option C).

By correctly using the center-of-mass frame for the second decay, the relative velocity of the daughter particle $D$ is found, which must then be vectorially added to the lab velocity of $B$ to find the maximum possible lab velocity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Relative Velocity in 1D
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free