Question

A sphere of radius $1.00\text{cm}$ is placed in the path of a parallel beam of light of large aperture. The intensity of the light is $0.50{\text{W/cm}}^2.$ If the sphere partially absorbs $(\alpha =0.25)$ the radiation falling on it, find the force exerted by the light beam on the sphere.

• A. $9.3\times {10}^{-7}\text{N}$
• B. $5.2\times {10}^{-7}\text{N}$
• C. $8.5\times {10}^{-7}\text{N}$
• D. $9.16\times {10}^{-9}\text{N}$

Answer 1

The correct option is D $9.16\times {10}^{-9}\text{N}$

$\text{Force}=\frac{IA}{c}(1+r)=\frac{\pi r^{2}I}{c}(1+r)$

Given, $I=0.5{\text{W/cm}}^2=5000{\text{W/m}}^2$
$r=1\text{cm}={10}^{-2}\text{m},c=3\times {10}^8\text{m/s}$
$\alpha =0.25\Rightarrow r=1-\alpha =1-0.25=0.75$

$\Rightarrow F=\frac{\pi \times ({10}^{-2}{)}^2\times 5000}{3\times {10}^8}\times (1+0.75)$

$\therefore F=9.16\times {10}^{-9}\text{N}$

Hence, $\left(C\right)$ is the correct answer.

Why this question? Caution: If $\alpha$ is given in the question, we can use the formula, $\text{Force}=\frac{IA(2-\alpha )}{c}$ Else, calculate, $r=1-\alpha$ for using the formula used in solution.