JEE Main 2023 · 12 April · morning · Single correct · +4 / −1
A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
- (a) 1 : 1
- (b) 1 : 4
- (c) 2 : 1
- (d) 1 : 3
Answer and solution
Answer (d) 1 : 3
Solution
Physics sir · 3 steps
PE goes as x², so at half the amplitude it is only a quarter of the total; KE takes the rest.
- Energy formulas. In SHM the potential energy is U = 1/2kx², and the total energy stays fixed at E = 1/2kA². Kinetic energy is whatever is left: K = E - U.
- Half the amplitude. Put x = A/2: U = 1/2k(A/2)² = 1/4×1/2kA² = E/4. So K = E - E/4 = 3E/4.
U/K = x²/(A² - x²) = (A²/4)/(3A²/4) = 1/3
- So. The ratio of potential energy to kinetic energy is 1 : 3, which is option (d).
The idea to keep. In SHM, U : K = x² : (A² - x²). Squaring is the whole game: half the displacement gives a quarter of the energy as PE, not half.
Answer from the NTA final answer key. Solution by PrepWiser.