What will be impact on the frequency of a simple pendulum if the length of pendulum is halved and value of gravity is doubled?
Correct answer: B. Doubled
- A. Halved
- B. Doubled
- C. Quadrupled
- D. None of these
Explanation
The frequency of a simple pendulum is given by: f = 1 / (2π) * √(g/L)where:f is the frequencyg is the acceleration due to gravityL is the length of the pendulumIf the length of the pendulum is halved (L/2) and the value of gravity is doubled (2g), the new frequency will be: f' = 1 / (2π) * √(2g / (L/2))Simplifying the equation: f' = 1 / (2π) * √(4g / L) f' = 2 * (1 / (2π) * √(g / L)) f' = 2fTherefore, the frequency of the pendulum will be doubled.
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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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