Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the sun respectively. The ratio of the pressure of solar radiation on sphere 2 to that on sphere 1 is
A) 0.25.
B) 0.50.
C) 1.0.
D) 2.0.
E) 4.0.

Question

Quizplus · Accepted Answer

The pressure of solar radiation on a surface is given by $P = \frac{2I}{c}$, where $I$ is the intensity of solar radiation (power per unit area) and $c$ is the speed of light. Since the spheres are identical, their areas are equal and the intensity of solar radiation is the same for both spheres.

The force on a sphere due to radiation pressure is given by $F = PA$, where $A$ is the area of the sphere. Since the spheres are identical, their areas are equal, so the force on sphere 2 is four times the force on sphere 1 (because the distance is doubled, the area of the sphere "seen" by the Sun is four times as large). Therefore, the ratio of the pressures on the two spheres is:

$$\frac{P_2}{P_1} = \frac{F_2/A}{F_1/A} = \frac{4F_1}{F_1} = 4 \cdot \frac{2I/c}{2I/c} = 4 \cdot 1 = 4$$

Therefore, the correct answer is A) 0.25, because the pressure on sphere 2 is one-fourth the pressure on sphere 1.

Two Identical Silver Spheres of Mass M and Radius R