Question

"A 500 kg rock is located on the Earth’s surface. If the mass of the moon is 7.4x10^22 kg, and the separation distance between the center of the rock and the center of the moon is 3.8x10^8 meters, what gravitational force does the moon exert on the rock? (Hint: the gravitational constant is equal to 6.67x10^-11 N * m^2 /kg)

A) 1.7x10^-2 Newtons
B) 8.6x10^-5 Newtons
C) 7.5x10 Newtons
D) 1.8x10^15 Newtons"

Please select the correct option.

Answer 1

The gravitational force that the moon exerts on a 500 kg rock on Earth's surface is calculated using Newton's Law of Universal Gravitation, yielding a force of approximately 8.6x10^-5 Newtons.

Step-by-step explanation:

To calculate the gravitational force that the moon exerts on a rock on Earth’s surface, we use Newton's Law of Universal Gravitation. The formula is given by F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1, and m2 are the masses of the two objects, and r is the distance between their centers. In this case, given that the mass of the moon (m2) is 7.4x10^22 kg, the mass of the rock (m1) is 500 kg, the separation distance (r) is 3.8x10^8 meters, and the gravitational constant (G) is 6.67x10^-11 N * m^2 / kg^2, we can substitute these values into the formula to find the gravitational force. F = (6.67x10^-11 N * m^2 / kg^2) * (500 kg * 7.4x10^22 kg) / (3.8x10^8 m)^2. Calculating this, we find that the force is approximately 8.6x10^-5 Newtons, which corresponds to option B.