The time period of a simple pendulum is 2 seconds. If its length is increased by 4 times, then its period becomes:
Correct answer: D. 4 sec
- A. 16 sec
- B. 12 sec
- C. 8 sec
- D. 4 sec
Explanation
The formula for the period of a simple pendulum is T = 2π √(l/g). The period is directly proportional to the square root of the length. Therefore, if the length is increased by 4 times, the period becomes √4 times the original period, which is 2 times. Hence, the original period of 2 seconds becomes 4 seconds. The other options are incorrect because they miscalculate the effect of the increased length on the period.
This question appeared on the ETEA MDCAT 2016 paper, which you can sit online with every answer explained.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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