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Question #43491

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m$ is constrained to move inside a smooth, straight, horizontal tube. The tube rotates in the horizontal plane about a fixed vertical axis passing through one of its ends. The angular velocity of the tube is given by $\omega = \alpha t$ , where $\alpha$ is a positive constant and $t$ is the time. The particle is pulled towards the axis of rotation at a constant relative speed $v_0$ by an internal mechanism. At $t = 0$ , the particle is at a distance $R$ from the axis. At what distance $r$ from the axis does the particle lose contact with the trailing wall of the tube and shift to the leading wall? (Assume the tube has vertical side walls and 'leading' refers to the wall facing the direction of rotation).

Options

A.
$\frac{2R}{3}$
B.
$\frac{R}{2}$
C.
$\frac{R}{3}$
D.
$\frac{3R}{4}$

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

Non-Uniform Circular Motion|Pseudo Force Directionality|Frame of Reference

Why This Question Is Tricky

Common Mistakes

This problem tests the student's ability to analyze non-uniform circular motion in a non-inertial reference frame, specifically focusing on the interplay between the Euler and Coriolis pseudo-forces.

A common trap is ignoring the Coriolis force entirely or missing its factor of 2 (which directly leads to the incorrect option R/2).

Furthermore, students often struggle with the vector directions of these forces.

Because the particle moves inward, the Coriolis force opposes the Euler force.

The 'lethal' aspect is recognizing that the normal constraint force is time-varying and vanishes exactly when these two velocity- and position-dependent pseudo-forces balance, requiring a simultaneous solution of the dynamic force balance and the kinematic constraint.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Non-Uniform Circular Motion
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free