Free Potential Energy MCQs with Answers

1. A ball is dropped from rest. Ignoring air resistance, as it falls its

• A. total mechanical energy increases
• B. potential energy converts into kinetic energy with the total unchanged
• C. kinetic energy converts into potential energy
• D. total mechanical energy decreases

Explanation: Gravity is a conservative force, so in the absence of air resistance the sum of kinetic and potential energy stays constant while potential energy is steadily converted into kinetic energy. With air resistance included the total mechanical energy would fall, the loss appearing as heat. Energy is never created, so the total cannot increase.

2. The gravitational potential energy gained by a 2 kg mass lifted through 5 m, taking g as 10 m s-2, is

• A. 10 J
• B. 25 J
• C. 100 J
• D. 1000 J

Explanation: Potential energy gained is mgh, which is 2 times 10 times 5, giving 100 J. The route taken to lift the mass makes no difference, since gravity is a conservative force and only the change in height counts. The answer 10 J comes from omitting the height.

3. The gravitational potential energy gained by a body of mass m raised through a height h near the Earth's surface is

• A. mgh
• B. half mgh
• C. mg divided by h
• D. mh

Explanation: The work done against a constant weight mg over a height h is mgh, and only the vertical height matters, not the path taken. Carrying a load up a ramp therefore requires the same work against gravity as lifting it straight up, though the force needed is smaller over a longer distance. Potential energy is always measured relative to a chosen zero level.

4. A body of mass 2 kg is raised 5 m. Taking g as 10 m per second squared, the potential energy gained is

• A. 10 J
• B. 50 J
• C. 100 J
• D. 25 J

Explanation: Using mgh, the energy is 2 multiplied by 10 multiplied by 5, giving 100 J. If the body were then dropped, all of it would convert to kinetic energy just before impact, giving a landing speed of 10 m per second. Forgetting to include g gives the 10 J distractor.

5. A ball is dropped from a height h. Just before it hits the ground, its speed is

• A. the square root of 2gh
• B. 2gh
• C. gh
• D. the square root of gh

Explanation: Equating the potential energy mgh to the kinetic energy half mv squared cancels the mass and gives v as the square root of 2gh, which is why all bodies fall at the same rate in the absence of air resistance. The same result follows from the equations of motion. Doubling the height increases the landing speed only by a factor of the square root of two.

6. The elastic potential energy stored in a spring stretched by extension x with spring constant k is

• A. kx
• B. half kx squared
• C. kx squared
• D. half kx

Explanation: The force rises linearly from zero to kx, so the average force is half of kx and the work done is half k x squared, which is also the area under the force extension graph. This is why doubling the extension quadruples the stored energy. The formula holds only while Hooke's law applies, that is below the elastic limit.

7. The work done by the gravitational force on an object as it moves from a reference level to a higher point is:

• A. Always positive
• B. Always negative
• C. Zero
• D. Depends on the path taken

Explanation: Gravity acts downwards while the displacement is upwards, so the force has a component opposite to the motion and the work it does is negative, which is exactly why the potential energy of the object increases. Coming back down, gravity does positive work. Because gravity is a conservative force, the work depends only on the change in height and not on the path.