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Question #42404

Difficulty: 8/10 | 🟢 Free

The Question

A smooth straight horizontal tube is fixed on a horizontal turntable rotating with a constant angular velocity $\omega$ about a vertical axis passing through a point $O$ . The shortest distance from $O$ to the tube is $d$ . Let $C$ be the point on the tube closest to $O$ . A particle of mass $m$ is released from rest relative to the tube at a point $A$ inside the tube, where the distance $AC = d$ . Find the work done by the tube on the particle in the ground frame by the time its distance from $O$ becomes $2d$ .

Options

A.
$(2 - \sqrt{2}) m\omega^2 d^2$
B.
$2 m\omega^2 d^2$
C.
$(3 - \sqrt{2}) m\omega^2 d^2$
D.
$m\omega^2 d^2$

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

Angular Velocity vs Linear Velocity|Pseudo Force Directionality|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This problem tests the application of the Work-Energy Theorem across inertial and non-inertial frames.

A common lethal mistake is assuming the normal force does zero work, which is only true in the rotating frame.

Students often attempt to calculate the work in the ground frame but fail to correctly transform the velocity vector using $\vec{v} = \vec{v}' + \vec{\omega} \times \vec{r}'$ , specifically forgetting the initial kinetic energy of the particle in the ground frame (leading to option C) or ignoring the centrifugal component of the normal force when integrating power directly (leading to option B).

The problem forces a rigorous vector analysis of Coriolis and centrifugal effects.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Angular Velocity vs Linear Velocity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free