If the mass of the Earth were to double, what would happen to the gravitational

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Question: If the mass of the Earth were to double, what would happen to the gravitational force between two objects on its surface?

Options:

Correct Answer: It would double

Solution:

F = G * (m1 * m2) / r², doubling the mass of Earth doubles the force.

If the mass of the Earth were to double, what would happen to the gravitational force between two objects on its surface?

If the mass of the Earth were to double, what would happen to the gravitational force between two objects on its surface?

Step 1: Understand the formula for gravitational force, which is F = G * (m1 * m2) / r².
Step 2: Identify what m1 and m2 represent in this formula. Here, m1 is the mass of the Earth and m2 is the mass of the other object.
Step 3: If the mass of the Earth (m1) doubles, we can represent this as 2 * m1.
Step 4: Substitute the new mass of the Earth into the formula: F = G * (2 * m1 * m2) / r².
Step 5: Notice that the new force (F) is now twice the original force because we have 2 * (G * (m1 * m2) / r²).
Step 6: Conclude that if the mass of the Earth doubles, the gravitational force between the two objects on its surface also doubles.

Gravitational Force – The gravitational force between two objects is determined by their masses and the distance between them, as described by Newton's law of universal gravitation.
Newton's Law of Universal Gravitation – This law states that the gravitational force (F) is proportional to the product of the masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers.