If the radius of the Earth were to double, what would happen to the gravitationa

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Question: If the radius of the Earth were to double, what would happen to the gravitational acceleration at its surface?

Options:

Correct Answer: It would be quartered

Solution:

Gravitational acceleration is inversely proportional to the square of the radius, so it would be quartered.

If the radius of the Earth were to double, what would happen to the gravitational acceleration at its surface?

If the radius of the Earth were to double, what would happen to the gravitational acceleration at its surface?

Correct Answer: Gravitational acceleration would be quartered.

Step 1: Understand that gravitational acceleration (g) depends on the mass of the Earth and the distance from its center (radius).
Step 2: Recall the formula for gravitational acceleration: g = G * (M / r^2), where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the Earth.
Step 3: Note that if the radius (r) doubles, it becomes 2r.
Step 4: Substitute 2r into the formula: g = G * (M / (2r)^2).
Step 5: Simplify the equation: (2r)^2 = 4r^2, so g = G * (M / 4r^2).
Step 6: This shows that the new gravitational acceleration is g/4, meaning it is one-fourth of the original value.
Step 7: Conclude that if the radius of the Earth doubles, the gravitational acceleration at its surface would be quartered.

Gravitational Acceleration – Gravitational acceleration at the surface of a planet is determined by the formula g = G * M / r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius.
Inverse Square Law – The gravitational force and acceleration are inversely proportional to the square of the distance from the center of the mass, meaning if the radius increases, the gravitational acceleration decreases significantly.