Pressure Exerted by Electromagnetic Waves and Mass

To determine the correct relationship between the Assertion (A) and Reason (R), let us analyze both statements independently:

1. Analysis of Assertion (A): An electromagnetic (EM) wave carries both energy $U$ and linear momentum $p$. The momentum $p$ carried by an electromagnetic wave of energy $U$ propagating in vacuum is given by: $p = \frac{U}{c}$ where $c$ is the speed of light in vacuum.

   When an electromagnetic wave strikes a surface, it transfers momentum to that surface. By Newton's second law, the force exerted on the surface is equal to the rate of transfer of momentum: $F = \frac{\Delta p}{\Delta t}$

   The radiation pressure ($P_{\text{rad}}$) exerted on a surface of area $A$ by an EM wave of intensity $I$ (for complete absorption) is given by: $P_{\text{rad}} = \frac{F}{A} = \frac{I}{c}$

   Therefore, electromagnetic waves exert pressure on any surface on which they fall. Thus, Assertion (A) is TRUE.

2. Analysis of Reason (R): Electromagnetic waves are composed of photons, which travel at the speed of light $c$ in vacuum. The rest mass ($m_0$) of a photon is zero ($m_0 = 0$). Therefore, there is no rest mass associated with electromagnetic waves. Thus, Reason (R) is TRUE.

3. Evaluating the Explanation: The reason EM waves exert pressure is that they carry momentum ($p = U/c$), which is transferred to the surface upon collision. The fact that EM waves have no rest mass is not the reason why they exert pressure; in fact, radiation pressure arises despite the absence of rest mass because momentum is associated with the wave's electromagnetic energy.

   Therefore, Reason (R) is NOT the correct explanation for Assertion (A).

Hence, Both (A) and (R) are true but (R) is not the correct explanation of (A).

Correct Answer: Option B