JEE Physics 2025 Question with Solution

Given: Power of source = $450 \, \text{W}$, distance = $2 \, \text{m}$, surface is perfectly reflecting.

Find: Radiation pressure on the surface.

For a perfectly reflecting surface,

$$P_{rad} = \frac{2I}{c}$$

where $I$ is the intensity and $c = 3 \times 10^8 \, \text{m/s}$.

The intensity at distance $r$ from an isotropic source is

$$I = \frac{P_{source}}{4\pi r^2}$$

Substituting the given values,

$$I = \frac{450}{4\pi (2)^2} = \frac{450}{16\pi}$$

So,

$$I \approx \frac{450}{50.27} \approx 8.95 \, \text{W/m}^2$$

Now the radiation pressure is

$$P_{rad} = \frac{2 \times 8.95}{3 \times 10^8}$$ $$P_{rad} \approx \frac{17.9}{3 \times 10^8} \approx 5.97 \times 10^{-8} \, \text{N/m}^2$$

Since $1 \, \text{N/m}^2 = 1 \, \text{Pa}$,

$$P_{rad} \approx 5.97 \times 10^{-8} \, \text{Pa} \approx 6 \times 10^{-8} \, \text{Pa}$$

the solution works out $6 \times 10^{-8} \, \text{Pa}$, but it also states that the correct option is C, whose listed value is $6 \times 10^{-5} \, \text{Pascals}$. This is a discrepancy in the source. Following the solution's declared correct option, the correct option is C.

Given: A $450 \, \text{W}$ light source and a perfectly reflecting surface at $2 \, \text{m}$.

Find: The radiation pressure.

1. Spread the source power over a spherical surface of radius $2 \, \text{m}$:

$$A = 4\pi r^2 = 4\pi (2)^2 = 16\pi \, \text{m}^2$$

2. Compute the intensity:

$$I = \frac{450}{16\pi} \approx 8.95 \, \text{W/m}^2$$

3. For perfect reflection, pressure is twice the absorbing case:

$$P_{rad} = \frac{2I}{c}$$

4. Substitute:

$$P_{rad} = \frac{2 \times 8.95}{3 \times 10^8} \approx 5.97 \times 10^{-8} \, \text{Pa}$$

Thus the numerical result from the working is $6 \times 10^{-8} \, \text{Pa}$.

However, the solution's explicitly says "The Correct Option is C" and option C is $6 \times 10^{-5} \, \text{Pascals}$. Therefore the source contains an internal inconsistency between its calculation and its listed answer. Using the page's declared option label, the answer is recorded as C.