If the amplitude of a simple pendulum is increased four times, then its time period will
Correct answer: B. Remain the same.
- A. Reduce to half.
- B. Remain the same.
- C. Increase two times.
- D. Decrease four times.
Explanation
The time period of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula shows that the time period is independent of the amplitude of the swing, provided the amplitude is small (small-angle approximation). Therefore, increasing the amplitude four times will not affect the time period, meaning it will remain the same. The incorrect options suggest changes in the time period, which contradict the properties of a simple pendulum.
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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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