Question

What is the total force acting on earth due to the solar radiation? Assume that the earth absorbs all of the incident radiations.
Given: radius of earth, $R=6400\text{km}$, intensity of solar radiations, $I=1.5{\text{kW/m}}^2$.

• A. $3.2\times {10}^8\text{N}$
• B. $3.2\times {10}^{10}\text{N}$
• C. $6.4\times {10}^8\text{N}$
• D. $6.4\times {10}^{10}\text{N}$

Answer 1

The correct option is C $6.4\times {10}^8\text{N}$

The radius of earth is very small compared to the distance between earth and sun.
So, the solar radiation incident on the earth's surface (on the hemisphere facing the sun) can be considered to be incident normally on an imaginary circle of radius $6400\text{km}$.

Now, $F=\frac{IA}{c}=\frac{1.5\times {10}^3\times \pi \times (64\times {10}^5{)}^2}{3\times {10}^8}$
$\approx 6.4\times {10}^8\text{N}$

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