Chapter 13, Problem 32A

Earth and the moon are gravitationally attracted to each other. Does the more massive Earth attract the moon with a greater force, the same force, or less force than the moon attracts Earth?

To determine

Whether more massive earth attracts moon with greater force, same force or less force.

Answer to Problem 32A

More massive earth attracts moon with greater force.

Explanation of Solution

Given:

Earth and Moon are attracted to each other due to gravity.

Formula used :

  $F=\frac{G{M}_1{M}_2}{R^2}$

Where, G is gravitational constant $M_1,M_2$ are masses of two different objects and R is distance between them.

Calculation :

Let mass of earth is $M_e$ and mass of moon is $M_m$ and distance between them is R.

Now, substituting the value of $M_1=M_e$ , $M_2=M_m$ and R.

  $F=\frac{G{M}_e{M}_m}{R^2}$

From the above expression it is clear that gravitational force is directly proportional to mass of earth therefore more massive earth attracts moon with greater force.

Conclusion :

Therefore, more massive earth attracts moon with greater force.