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For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (The graphs are schematic and not drawn to scale.)
Asked in JEE Main 2015 · Energy graphs
- (1) KE drawn as an upward parabola in d and PE as a downward one
- (2) both curves drawn as exponentials in |d|
- (3) both curves rising as |d| increases
- (4) PE an upward parabola from zero at d=0, KE a downward parabola from its maximum at d=0, the two crossing and summing to a constant
Answer: (4) PE an upward parabola from zero at d=0, KE a downward parabola from its maximum at d=0, the two crossing and summing to a constant
Step-by-step solution
For small oscillations U=1/2 kd², an upward parabola with its minimum at d=0.
K=E-U is then a downward parabola, greatest at d=0 and zero at d=± A; the two cross where each equals E/2.
Why the other options are wrong
- (1) Swaps the two labels: it is the potential energy that grows with displacement.
- (2) Exponential curves do not follow from U∝ d².
- (3) Both cannot rise together, because their sum must stay constant.
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