A body has a free fall from a height of 20 m. After falling through a distance of 5 m, the body would<\/p>\n
[amp_mcq option1=”lose one-fourth of its total energy” option2=”lose one-fourth of its potential energy” option3=”gain one-fourth of its potential energy” option4=”gain three-fourth of its total energy” correct=”option2″]<\/p>\n
After falling 5 m (at 15 m height):
\nPotential Energy at 15m = PE’ = mgh = mg(15).
\nThe loss in potential energy is Initial PE – PE’ = 20mg – 15mg = 5mg.
\nThe fraction of the *initial* potential energy lost is (Loss in PE) \/ (Initial PE) = (5mg) \/ (20mg) = 1\/4.<\/p>\n
By conservation of energy, the energy lost from potential energy is gained as kinetic energy.
\nKE gained = Loss in PE = 5mg.
\nKinetic Energy at 15m = KE’ = 5mg.
\nTotal Energy at 15m = PE’ + KE’ = 15mg + 5mg = 20mg. The total energy remains constant.<\/p>\n
Let’s evaluate the options:
\nA) lose one-fourth of its total energy: Incorrect, total energy is conserved.
\nB) 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.
\nC) gain one-fourth of its potential energy: Incorrect, potential energy decreases as the body falls.
\nD) gain three-fourth of its total energy: Incorrect, total energy is conserved.<\/p>\n