Before You Begin

Question #43708

Difficulty: 8/10 | 🟢 Free

The Question

A stationary nucleus of mass $2m$ undergoes nuclear fission into two identical fragments, each of mass $m$ . The total mass defect of the reaction corresponds to an energy equivalent $Q$ . During the fission process, a gamma-ray photon of energy $E_\gamma$ is emitted. Assume the momentum carried by the gamma-ray photon is negligible. One of the fission fragments enters a medium where it experiences a velocity-dependent drag force of magnitude $F_d = kv^2$ (where $k$ is a positive constant and $v$ is the instantaneous velocity) in addition to a constant kinetic friction force of magnitude $f_k = \mu mg$ , where $\mu$ is the coefficient of kinetic friction and $g$ is the acceleration due to gravity. Which of the following expressions gives the total distance $x$ traveled by this fragment before coming to rest?

Options

A.
$\frac{m}{2k} \ln\left( 1 + \frac{k (Q - E_\gamma)}{\mu m^2 g} \right)$
B.
$\frac{m}{2k} \ln\left( 1 + \frac{k Q}{\mu m^2 g} \right)$
C.
$\frac{m(Q - E_\gamma)}{2[k(Q - E_\gamma) + \mu m^2 g]}$
D.
$\frac{m}{2k} \ln\left( 1 + \frac{2k (Q - E_\gamma)}{\mu m^2 g} \right)$

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

Nuclear Fission Energy Balance|Work Done by Friction|Work-Energy Theorem Validity

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to synthesize nuclear energy balance with non-uniform mechanics.

A common trap is blindly applying the Work-Energy Theorem assuming a constant drag force (e.g., evaluating drag only at the initial velocity), which ignores the path-dependent nature of $F_d = -kv^2$ and bypasses the necessary differential equation $v \frac{dv}{dx}$ .

Additionally, students often fail to subtract the gamma-ray emission energy $E_\gamma$ from the total mass-defect $Q$ -value, incorrectly assuming all nuclear energy manifests as mechanical kinetic energy of the fragments.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Nuclei - Class 12
Concept	Nuclear Fission Energy Balance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free