A body has a free fall from a height of 20 m. After falling through a distance of 5 m, the body would
We use the principle of conservation of mechanical energy, assuming no air resistance. Total Mechanical Energy (TE) = Potential Energy (PE) + Kinetic Energy (KE).
Initial state (at 20 m height):
Initial PE = mgH = mg(20).
Initial KE = 0 (free fall starts from rest).
Initial TE = mg(20) + 0 = 20mg.
After falling 5 m (at 15 m height):
Potential Energy at 15m = PE’ = mgh = mg(15).
The loss in potential energy is Initial PE – PE’ = 20mg – 15mg = 5mg.
The fraction of the *initial* potential energy lost is (Loss in PE) / (Initial PE) = (5mg) / (20mg) = 1/4.
By conservation of energy, the energy lost from potential energy is gained as kinetic energy.
KE gained = Loss in PE = 5mg.
Kinetic Energy at 15m = KE’ = 5mg.
Total Energy at 15m = PE’ + KE’ = 15mg + 5mg = 20mg. The total energy remains constant.
Let’s evaluate the options:
A) lose one-fourth of its total energy: Incorrect, total energy is conserved.
B) lose one-fourth of its potential energy: The initial potential energy was 20mg. The loss is 5mg, which is indeed one-fourth (1/4) of the initial potential energy. Correct.
C) gain one-fourth of its potential energy: Incorrect, potential energy decreases as the body falls.
D) gain three-fourth of its total energy: Incorrect, total energy is conserved.
Note: If the question meant “lose one-fourth of its *remaining* potential energy”, that would be different, but the phrasing “lose one-fourth of its total potential energy” usually refers to the initial maximum potential energy.