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Question #42373

Difficulty: 8/10 | 🟢 Free

The Question

A uniform rigid rod of mass $M$ and length $L$ is placed in a smooth straight radial groove on a horizontal turntable. The turntable rotates at a constant angular velocity $\omega$ about a vertical axis passing through its center. Initially, the rod is held at rest relative to the turntable with its inner end at a distance $r_0$ from the rotation axis. The rod is then released. What is the total work done by the normal force exerted by the groove on the rod in the inertial frame of reference, from the moment of release until its inner end reaches a distance $2r_0$ ?

Options

A.
$M \omega^2 r_0 (3r_0 + L)$
B.
$\frac{1}{2} M \omega^2 r_0 (3r_0 + L)$
C.
$0$
D.
$M \omega^2 r_0 (2r_0 + L)$

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

Rigid Body Constraints|Variable Force Integration|Frame of Reference

Why This Question Is Tricky

Common Mistakes

This problem tests the rigorous application of the Work-Energy Theorem across inertial and non-inertial reference frames, specifically focusing on the integration of variable pseudo-forces (Coriolis and Centrifugal) over a rigid body.

The primary trap is assuming that the normal force does zero work, which is only true in the rotating frame.

A secondary 'lethal' trap is calculating the change in rotational kinetic energy $\Delta(\frac{1}{2}I\omega^2)$ and assuming it equals the total work done by the groove, completely neglecting the radial kinetic energy $\frac{1}{2}M v_{rel}^2$ gained due to the centrifugal force.

By forcing the integration of the Coriolis power $P = \int dN(\omega x)$ over the varying radius $r(t)$ , the question eliminates students who rely on standard constant-force kinematic equations or incomplete energy conservation setups.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Rigid Body Constraints
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free