Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :} The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.
Reason (R) :} There is no mass associated with the electromagnetic waves.
In the light of the above statements, choose the correct answer from the options given below :

• A. Both (A) and (R) are true and (R) is the correct explanation of (A)
• B. Both (A) and (R) are true but (R) is not the correct explanation of (A)
• C. (A) is true but (R) is false
• D. (A) is false but (R) is true

Hint:

Recall the relation between energy and momentum for a massless particle, $p=E/c$, and remember that pressure comes from the rate of momentum transfer, $F=dp/dt$. Then ask whether "no mass" or "momentum" is the actual cause of the pressure.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Electromagnetic waves carry momentum ($p = U/c$). When they hit a surface, they transfer this momentum, creating radiation pressure. They are composed of photons which have zero rest mass.
Step 2: Detailed Explanation:
Assertion: True. Radiation pressure $P = I/c$ (for total absorption) or $2I/c$ (for reflection) exists because EM waves carry momentum.
Reason: True. Photons have zero rest mass. Energy is related to frequency, not mass.
Explanation check: The pressure exists because of momentum, not because of the absence of mass. Therefore, (R) is not the reason why (A) is true.
Step 3: Final Answer:
Both are true but (R) is not the correct explanation of (A).

Answer 2

Concept:

• A photon has zero rest mass, but the relativistic energy-momentum relation $E^2 = (pc)^2 + (mc^2)^2$ reduces to $E = pc$ when $m=0$, so a massless photon still carries momentum $p = E/c$.
• Pressure on a surface arises from the rate of change of momentum delivered to it, $F = \dfrac{dp}{dt}$, regardless of whether the particles carrying that momentum have mass.

Step 1: Check the momentum carried by an electromagnetic wave.
An electromagnetic wave is made of photons, each with energy $E=h\nu$ and momentum $p = \dfrac{E}{c} = \dfrac{h\nu}{c}$.
This momentum exists even though each photon has zero rest mass.

Step 2: Connect momentum delivery to pressure.
When photons strike a surface and are absorbed or reflected, they transfer momentum to it.
Force on the surface is the rate of this momentum transfer, $F = \dfrac{dp}{dt}$, and pressure is this force per unit area.
This confirms that electromagnetic waves do exert pressure, so Assertion (A) is true.

Step 3: Check the truth of Reason (R) on its own.
Photons are indeed massless particles, since they always travel at speed $c$ and a massive particle cannot do so.
So Reason (R) is also true as a standalone statement.

Step 4: Check whether (R) actually explains (A).
Radiation pressure exists because photons carry momentum, $p=E/c$, not because they lack mass.
Many massless things exert no pressure at all; what matters here is the momentum term, not the absence of mass.
So (R), while true, is not the reason behind (A).

Final Answer: Both (A) and (R) are true but (R) is not the correct explanation of (A).