Question

The force F keeping the moon in its orbit around the earth is inversely proportional to the square of the distance r from the earth. If F = 6 x 10^5 KN, and r = 8 x 10^6 m, find the equation connecting F and r.

a) F = k / r^2, where k is a constant.
b) F = k * r^2, where k is a constant.
c) F = 6 x 10^5 * 8 x 10^6, representing the relationship between F and r.
d) F = 6 x 10^5 + 8 x 10^6, representing the relationship between F and r.

Answer 1

The force keeping the moon in its orbit around the earth is inversely proportional to the square of the distance from the earth.

Step-by-step explanation:

The force keeping the moon in its orbit around the earth is inversely proportional to the square of the distance from the earth. This relationship can be expressed as F = k / r^2, where F is the force, r is the distance, and k is a constant. To find the value of k, we can substitute the given values of F and r into the equation. F = 6 x 10^5 KN and r = 8 x 10^6 m, so k = F x r^2 = (6 x 10^5 KN) x (8 x 10^6 m)^2 = 3.84 x 10^36. Therefore, the equation connecting F and r is F = (3.84 x 10^36) / r^2.