If the radius of the Earth is doubled, what will happen to the gravitational for

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Question: If the radius of the Earth is doubled, what will happen to the gravitational force experienced by an object on its surface?

Options:

Correct Answer: It will be quartered

Solution:

Gravitational force is inversely proportional to the square of the radius. If radius is doubled, F becomes F/4.

If the radius of the Earth is doubled, what will happen to the gravitational force experienced by an object on its surface?

If the radius of the Earth is doubled, what will happen to the gravitational force experienced by an object on its surface?

Step 1: Understand that gravitational force depends on the mass of the Earth and the distance from its center.
Step 2: Know that the formula for gravitational force (F) is F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 is the mass of the Earth, m2 is the mass of the object, and r is the radius of the Earth.
Step 3: Recognize that if the radius (r) is doubled, it becomes 2r.
Step 4: Substitute 2r into the formula: F = G * (m1 * m2) / (2r)^2.
Step 5: Simplify (2r)^2 to get 4r^2, so the formula now is F = G * (m1 * m2) / 4r^2.
Step 6: Notice that the new gravitational force is F/4, meaning it is reduced to a quarter of the original force.

Gravitational Force – The gravitational force experienced by an object is determined by the mass of the object and the mass of the Earth, and it is inversely proportional to the square of the distance from the center of the Earth.
Inverse Square Law – This law states that the force of gravity decreases with the square of the distance; thus, if the radius is doubled, the gravitational force is reduced to a quarter of its original value.