If the mass of an object is halved and the distance from the center of the Earth is doubled, what happens to the gravitational potential energy?

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Q: If the mass of an object is halved and the distance from the center of the Earth is doubled, what happens to the gravitational potential energy?

Solution: Gravitational potential energy is directly proportional to mass and inversely proportional to distance, so it halves.

Steps: 7

Step 1: Understand that gravitational potential energy (GPE) depends on two things: mass and distance from the center of the Earth.
Step 2: Remember the formula for gravitational potential energy: GPE = (mass * gravitational constant * height).
Step 3: If the mass is halved, it means we multiply the mass by 0.5.
Step 4: If the distance from the center of the Earth is doubled, it means we multiply the height by 2.
Step 5: When we calculate the new GPE, we have: New GPE = (0.5 * mass * gravitational constant * (2 * height)).
Step 6: Simplifying this gives us: New GPE = (0.5 * mass * gravitational constant * height * 2) = mass * gravitational constant * height.
Step 7: This shows that the new GPE is equal to the original GPE, meaning it does not change.