Question

The gravitational force with which the earth attracts the moon:
(A) is less than the force with which the moon attracts the earth.
(B) is equal to the force with which the moon attracts the earth.
(C) is greater than the force with which the moon attracts the earth.
(D) Varies with the phases of the moon.

Answer 1

- Hint: One of Newton's laws states that for every action there is equal and opposite reaction. In simple statements, if the force is applied to the body then the body also applies an equal magnitude force opposite the direction of the force applied to it. This law is applicable for all bodies in the whole world.

Complete step-by-step solution
Newton states his third law as every object in the world reacts with equal force when the force applies to it. Consider the system of the earth and the moon. Because of the gravitational force every object near the earth is forced towards the earth, even the objects which are very far away from the earth. So, the gravitational force which earth attracts the moon, the moon attracts the earth with the same force.

So, the correct answer is (B).

Additional Information:
In this system both the objects have mass so the gravitational force between them is, \[F=\dfrac{G{{M}_{1}}{{M}_{2}}}{{{R}^{2}}}\]
For the earth moon system,
 \[{{F}_{{e}/{m}\;}}=\dfrac{G{{M}_{e}}{{M}_{m}}}{{{R}^{2}}}\]and \[{{F}_{{m}/{e}\;}}=-\dfrac{G{{M}_{e}}{{M}_{m}}}{{{R}^{2}}}\], here negative sign stands for opposite direction.

Note: From the universal law, Newton’s third law of motion the gravitational forces from the earth to the moon and the moon to the earth are equal but opposite in direction. Since the formula of the gravitational force depends on both objects masses then the formula is applicable for both objects as well.