Question

When a satellite is on the surface of a planet, it experiences a gravitational force $W$. What is the gravitational force when the satellite is at height $R/50$, where $R$ is the radius of the planet?

• A. 1.02 W
• B. 1.00 W
• C. 0.92 W
• D. 0.96 W

Hint:

The gravitational force decreases with the square of the distance from the center of the planet.

Answer 1

The Correct Option is D

The gravitational force at a height $h$ from the surface of the planet is given by: \[ F = \frac{W}{(1 + \frac{h}{R})^2} \] where $W$ is the gravitational force at the surface of the planet, and $R$ is the radius of the planet. For $h = R/50$, we get: \[ F = \frac{W}{(1 + \frac{1}{50})^2} \approx 0.96W \]