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Question #43147

Difficulty: 8/10 | 🟢 Free

The Question

A uniform solid circular disk of mass $M$ and radius $R$ is initially at rest in an inertial laboratory frame. It is free to rotate about its fixed central vertical axis without friction. A laser mounted on the edge of the disk fires a short tangential light pulse of total energy $E$ , causing the disk to recoil. After the disk reaches a steady angular velocity, a second laser located exactly at the center of the disk emits a short light pulse. This central laser is fixed to the disk and points radially towards a small detector also fixed on the edge of the disk. What is the arc length distance along the edge of the disk by which the central light pulse misses the detector? (Assume the speed of light is $c$ and the disk's rotational speed satisfies $v \ll c$ ).

Options

A.
$\frac{ER}{Mc^2}$
B.
$\frac{2ER}{Mc^2}$
C.
0
D.
$\frac{4ER}{Mc^2}$

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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

Ray Tracing for Systems|Angular Velocity vs Linear Velocity|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of angular momentum conservation with the kinematics of light in rotating frames.

A primary trap is the misapplication of Galilean velocity addition to light: students often incorrectly assume the rotating central laser imparts a tangential velocity component to the photon (like a bullet fired from a rotating turret), which would lead to a deviation of zero.

A secondary trap lies in the rotating frame analysis; students who correctly identify the need for fictitious forces frequently omit the factor of 2 in the Coriolis acceleration ( $a_c = 2\omega c$ ), or mistakenly use the moment of inertia of a ring instead of a solid disk, both of which lead to an answer off by a factor of two.

The problem demands strict adherence to the invariance of the speed of light in the inertial lab frame and precise application of rigid body dynamics.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Ray Tracing for Systems
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free