If an object is moved to a height equal to the radius of the Earth, how does the

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Question: If an object is moved to a height equal to the radius of the Earth, how does the gravitational force acting on it change?

Options:

Correct Answer: It becomes one-fourth

Solution:

At a height equal to the radius of the Earth, the gravitational force becomes one-fourth of its value at the surface.

If an object is moved to a height equal to the radius of the Earth, how does the gravitational force acting on it change?

If an object is moved to a height equal to the radius of the Earth, how does the gravitational force acting on it change?

Step 1: Understand that gravity pulls objects towards the center of the Earth.
Step 2: Know that the gravitational force depends on the distance from the center of the Earth.
Step 3: The radius of the Earth is the distance from the center of the Earth to its surface.
Step 4: If you move an object to a height equal to the radius of the Earth, you are now twice the distance from the center of the Earth (radius + radius = 2 radii).
Step 5: Use the formula for gravitational force: F = G * (m1 * m2) / r^2, where r is the distance from the center of the Earth.
Step 6: At the surface of the Earth, the distance (r) is 1 radius. At the height equal to the radius of the Earth, the distance (r) is 2 radii.
Step 7: When you double the distance (from 1 radius to 2 radii), the gravitational force becomes 1/(2^2) = 1/4 of the original force.

Gravitational Force Variation with Height – The gravitational force decreases with the square of the distance from the center of the Earth, which is relevant when calculating the force at different heights.
Inverse Square Law – Understanding that gravitational force follows an inverse square law, meaning if the distance from the center of the Earth doubles, the gravitational force becomes one-fourth.