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Question #43600

Difficulty: 8/10 | 🟢 Free

The Question

A uniform semi-circular plate of mass $m$ and radius $R$ acts as an ideal linear polarizer. It is mounted on a frictionless spherical pivot at its center of curvature $O$ , allowing it to rotate freely in all directions. At a specific instant, the plate lies exactly in the space-fixed $XY$ -plane and is rotating with an angular velocity $\vec{\omega} = \omega_0 \hat{k}$ . The straight edge of the semi-circle lies along the $x'$ -axis of the body-fixed frame, and its transmission axis is parallel to this straight edge. A broad, uniform beam of linearly polarized light of intensity $I_0$ propagates in the $-Z$ direction, with its electric field polarized along the space-fixed $X$ -axis. If at this instant the straight edge makes an angle $\phi = \pi/4$ with the $X$ -axis, what is the magnitude of the instantaneous angular acceleration of the plate? (Assume the plate absorbs all light that is not transmitted, and $c$ is the speed of light).

Options

A.
$\frac{4 I_0 R}{3 m c}$
B.
$\frac{2 I_0 R}{3 m c}$
C.
$\frac{8 I_0 R}{3 m c}$
D.
$\frac{I_0 R}{3 m c}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Malus's Law|Angular Momentum Conservation|Torque about non-fixed axes

Why This Question Is Tricky

Common Mistakes

Students incorrectly apply the scalar form of Newton's Second Law for rotation ( $\tau = I\alpha$ ) using the moment of inertia about the current axis of rotation ( $I_{z'z'} = \frac{1}{2}mR^2$ ).

They fail to recognize that the radiation pressure creates a torque vector in the plane of the plate (specifically along the $x'$ -axis), which necessitates using the inertia tensor component for that specific axis ( $I_{x'x'} = \frac{1}{4}mR^2$ ) via Euler's equations.

Furthermore, the problem tests the correct application of Malus's law to find the absorbed (not transmitted) intensity and the geometric knowledge that the center of pressure for a uniform beam on a semi-circle lies at its centroid, generating the torque.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Wave Optics - Class 12
Concept	Malus's Law
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free