A sphere of radius 1.00 cm is placed in the path of a parallel beam of light of large aperture. The intensity of the light is 0.50 W `cm^-2`. If the sphere completely absorbs the radiation falling on it, find the force exerted by the light beam on the sphere.

Explanation

To find the force exerted by the light beam on the sphere, we can use the relationship between intensity, area, and force. Here’s a step-by-step solution:

### Step 1: Understand the Given Data
- Radius of the sphere, \( r = 1.00 \, \text{cm} = 0.01 \, \text{m} \)
- Intensity of the light, \( I = 0.50 \, \text{W/cm}^2 = 50 \, \text{W/m}^2 \) (since \( 1 \, \text{cm}^2 = 10^{-4} \, \text{m}^2 \))

### Step 2: Calculate the Area of the Sphere
The area \( A \) of the sphere that is exposed to the light can be calculated using the formula for the surface area of a sphere:
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