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

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

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

Steps: 6

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.