Chapter 7, Problem 8TE

What do you say to a friend who says that if gravity follows the inverse–square law, when you are on the 20^th floor of a building gravity on you should be one–fourth as much as when you're on the 10^th floor?

To determine

Whether the gravity on the 20th floor is one-fourth the gravity of the 10th floor due to inverse-square law of the gravity.

Answer to Problem 8TE

The friend's assumption about the force of gravity at 20^th floor and 10^th floor is wrong because the mass of the body is negligible as compared to Earth and Earth exerts same pull on both the floor.

Explanation of Solution

The gravity follows the inverse–square law, so the force of gravity varies with the distance. If the distance increases then the force of gravity decrease and force of gravity increase due to the decrease in the distance.

The force of gravity also depends on the mass of the objects. If the mass of the heavy object such that the mass of the light object become negligible, then the heavy object always attracts the light object with the same force of gravity and inverse–square law does not hold good.

The mass of the body compared to the Earth is negligible, so the force of gravity for the body is same at 20^th floor and 10^th floor of the building because Earth exerts the same pull at 20^th floor and 10^th floor of the building.

Conclusion:

Therefore, The friend's assumption about the force of gravity at 20^th floor and 10^th floor is wrong because the mass of the body is negligible as compared to Earth and Earth exerts same pull on both the floor.