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Question #43280

Difficulty: 8/10 | 🟢 Free

The Question

A cylindrical ferromagnetic rotor of moment of inertia $I = 0.05 \text{ kg m}^2$ and volume $V = 2 \times 10^{-4} \text{ m}^3$ is spinning freely at an initial angular velocity $\omega_0 = 120 \text{ rad/s}$ inside a stator. The stator produces a constant-magnitude magnetic field that causes the rotor material to undergo exactly one complete B-H hysteresis cycle per mechanical revolution. The area of the B-H hysteresis loop for the rotor material is $A_H = 500\pi \text{ J/m}^3$ . Assuming all other losses (such as bearing friction and eddy currents) are negligible, what is the time $t$ taken for the rotor to come to a complete stop?

Options

A.
$120 \text{ s}$
B.
$\frac{60}{\pi} \text{ s}$
C.
$240 \text{ s}$
D.
$\infty$

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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

Hysteresis Loop Area|Gyroscopic Stability|Mechanical Energy Conservation

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of macroscopic energy dissipation mechanisms in magnetic materials and their mechanical consequences.

A common trap is confusing hysteresis loss with eddy current loss.

Eddy current power dissipation scales with $\omega^2$ , which would result in a velocity-dependent retarding torque ( $\tau \propto \omega$ ) and an exponential decay of angular velocity, leading to the incorrect conclusion that the rotor never completely stops ( $t \to \infty$ ).

By recognizing that hysteresis energy loss per cycle is constant (Area of B-H loop $\times$ Volume), students must deduce that the retarding torque is constant, allowing the use of simple constant-acceleration kinematics to find a finite stopping time.

Another common error is omitting the $2\pi$ factor by confusing angular frequency with standard frequency, leading to incorrect scalar times.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Magnetism and Matter - Class 12
Concept	Hysteresis Loop Area
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free