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

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Question: If the radius of the Earth were to double, what would happen to the weight of an object on its surface?

Options:

Correct Answer: It would become four times less

Solution:

Weight is proportional to 1/r^2; if the radius doubles, the weight becomes four times less.

If the radius of the Earth were to double, what would happen to the weight of an object on its surface?

If the radius of the Earth were to double, what would happen to the weight of an object on its surface?

Step 1: Understand that weight is the force of gravity acting on an object.
Step 2: Know that the force of gravity depends on the mass of the Earth and the distance from the center of the Earth.
Step 3: The formula for weight (W) is W = 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 4: If the radius of the Earth doubles, the new radius (r') is 2r.
Step 5: Substitute the new radius into the weight formula: W' = G * (m1 * m2) / (2r)^2.
Step 6: Simplify the equation: W' = G * (m1 * m2) / (4r^2).
Step 7: Notice that W' is 1/4 of the original weight (W), meaning the weight becomes four times less.

Gravitational Force – The weight of an object is determined by the gravitational force acting on it, which is inversely proportional to the square of the distance from the center of the Earth.
Inverse Square Law – The relationship that states that the force of gravity decreases with the square of the distance from the center of the mass.