Answer to Question #121139 in Classical Mechanics for Lizwi

Question

A baseball is located at the surface of the earth. Which statements about it are correct? (There may be more than one correct choice.)
1 : The earth exerts a much greater gravitational force on the ball than the ball exerts on the earth.
2 : The ball exerts a greater gravitational force on the earth than the earth exerts on the ball.
3 : The gravitational force on the ball due to the earth is exactly the same as the gravitational force on the earth due to the ball.
4 : The gravitational force on the ball is independent of the mass of the ball.
5 : The gravitational force on the ball is independent of the mass of the earth

Answer 1

Only correct statement is (3).

Because,

Let, mass of earth and baseball are M and m respectively and distance between them (center to center) is d.

Thus,according to Newton's law of gravitation, Force between earth and baseball is

$$F_{eb}=G\frac{Mm}{d^2}$$

acting along the direction of center of earth while force between baseball and earth is

$$F_{be}=G\frac{Mm}{d^2}$$

acting along the direction of center of base ball.

Clearly,

$$F_{eb}=F_{be}$$