Question

Light with energy flux 36W/cm² is incident on a well polished metal square plate of side 2cm. The force experienced by it is:

• A. 0.96μN
• B. 0.24 μN

Answer 1

Answer: (A)

0.96μN

Answer 2

The problem asks us to calculate the force experienced by a well-polished metal square plate when light with a given energy flux is incident on it.

1. Identify Given Parameters and Convert to SI Units:

• Energy flux (intensity), $I = 36 \text{ W/cm}^2$. To convert to W/m$^2$: $I = 36 \text{ W/cm}^2 \times \left(\frac{100 \text{ cm}}{1 \text{ m}}\right)^2 = 36 \times 10^4 \text{ W/m}^2$
• Side of the square plate, $s = 2 \text{ cm}$. To convert to meters: $s = 2 \times 10^{-2} \text{ m}$
• Area of the square plate, $A = s^2 = (2 \times 10^{-2} \text{ m})^2 = 4 \times 10^{-4} \text{ m}^2$.
• Speed of light, $c = 3 \times 10^8 \text{ m/s}$.
• The plate is "well polished metal", which means it is a perfectly reflecting surface.

2. Formula for Force due to Radiation Pressure: For a perfectly reflecting surface, the force $F$ exerted by light incident normally on a surface of area $A$ with intensity $I$ is given by: $F = \frac{2IA}{c}$

3. Calculate the Force: Substitute the values into the formula: $F = \frac{2 \times (36 \times 10^4 \text{ W/m}^2) \times (4 \times 10^{-4} \text{ m}^2)}{3 \times 10^8 \text{ m/s}}$ $F = \frac{2 \times 36 \times 4 \times 10^{4-4}}{3 \times 10^8}$ $F = \frac{2 \times 36 \times 4 \times 10^0}{3 \times 10^8}$ $F = \frac{288}{3 \times 10^8}$ $F = \frac{96}{10^8}$ $F = 96 \times 10^{-8} \text{ N}$

4. Convert to Micro Newtons (μN): Since $1 \text{ μN} = 10^{-6} \text{ N}$: $F = 96 \times 10^{-8} \text{ N} = 0.96 \times 10^{-6} \text{ N}$ $F = 0.96 \text{ μN}$

The final answer is 0.96μN.