If the radius of the Earth is doubled, what will be the change in gravitational

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Question: If the radius of the Earth is doubled, what will be the change in 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 the radius is doubled, the force becomes 1/4 of the original.

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

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

Step 1: Understand that gravitational force depends on the mass of the objects and the distance between them.
Step 2: Know that the formula for gravitational force (F) is F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance (radius).
Step 3: Recognize that if the radius (r) of the Earth is doubled, it becomes 2r.
Step 4: Substitute 2r into the formula: F = G * (m1 * m2) / (2r)^2.
Step 5: Simplify the equation: (2r)^2 = 4r^2, so F = G * (m1 * m2) / 4r^2.
Step 6: Notice that the new gravitational force is now 1/4 of the original force because of the 4 in the denominator.
Step 7: Conclude that if the radius of the Earth is doubled, the gravitational force experienced by an object on its surface becomes 1/4 of what it was originally.

Gravitational Force – Gravitational force is determined by the formula 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.
Inverse Square Law – The gravitational force decreases with the square of the distance between the centers of two masses, meaning if the radius is doubled, the force is reduced to a quarter of its original value.