Before You Begin

Question #43603

Difficulty: 8/10 | 🟢 Free

The Question

A perfectly reflecting light sail of rest mass $m_0$ and cross-sectional area $A$ is propelled in a vacuum by a stationary laser beam of constant intensity $I$ . The laser beam is directed normally to the surface of the sail. Assuming the sail moves purely translationally along the direction of the laser beam, what is the instantaneous acceleration of the sail at the moment its velocity reaches $v = \frac{3}{5}c$ (where $c$ is the speed of light in vacuum) relative to the laser?

Options

A.
$\frac{32 I A}{125 m_0 c}$
B.
$\frac{128 I A}{125 m_0 c}$
C.
$\frac{I A}{2 m_0 c}$
D.
$\frac{2 I A}{m_0 c}$

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

Photon Neutrality|The Velocity-Position Identity|Calculus-based Approximation

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of relativistic electrodynamics and relativistic mechanics.

Students commonly fall into two traps: (1) They use the classical radiation pressure $F = 2I/c$ without accounting for the relativistic Doppler shift of the photon flux and energy, which reduces the effective intensity on a receding boundary by a factor of $(c-v)/(c+v)$ . (2) They incorrectly apply Newton's second law as $F = m_0 a$ or $F = \gamma m_0 a$ , failing to recognize that the derivative of relativistic momentum $p = \gamma m_0 v$ with respect to time yields a longitudinal inertial mass of $\gamma^3 m_0$ .

The correct solution requires balancing the Doppler-modified radiation force with the correct relativistic rate of change of momentum.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Dual Nature of Radiation and Matter - Class 12
Concept	Photon Neutrality
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free