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Question #42389

Difficulty: 8/10 | 🟢 Free

The Question

A uniform conducting rod of mass $m$ and length $l$ is pivoted at one of its ends $O$ and can rotate freely in a horizontal plane. A uniform vertical magnetic field $B$ exists in the region. The free end of the rod slides on a fixed, smooth, perfectly conducting circular ring of radius $l$ centered at $O$ . A resistor of resistance $R$ is connected between the pivot $O$ and the ring. The rod has negligible resistance. At $t = 0$ , an angular impulse $J$ is applied to the rod about the pivot. What is the total angle rotated by the rod before it comes to a complete stop?

Options

A.
$\frac{4 J R}{B^2 l^4}$
B.
$\frac{2 J R}{B^2 l^4}$
C.
$\frac{3 J R}{B^2 l^4}$
D.
$\frac{8 J R}{B^2 l^4}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Impulsive Torque and Angular Momentum|Motional EMF in Rotating Rods|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the ability to model a velocity-dependent non-conservative force (magnetic braking) and correctly apply the torque-angular momentum relations.

A common trap is attempting to use energy conservation by equating initial kinetic energy to total Joule heating, which leads to a complex integral of $\omega^2(t)$ over time.

Students often fail to recognize that the damping torque is strictly proportional to $\omega$ , allowing the differential equation $I \omega d\omega/d\theta = -k\omega$ to be simplified to $I d\omega/d\theta = -k$ .

By transforming the time-domain differential equation into the angular domain, the integration becomes trivial and independent of the moment of inertia's explicit form.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Impulsive Torque and Angular Momentum
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free