If T is to be increased to 3T then length of pendulum should be increased by:
Correct answer: A. 9 times
- A. 9 times
- B. 8 times
- C. 10 times
- D. 20 time
Explanation
The time period of a simple pendulum is given by: T = 2π√(L/g)where:T is the time periodL is the length of the pendulumg is the acceleration due to gravityIf we want to increase the time period to 3T, we need to increase the length of the pendulum by a factor of 9. This is because the time period is proportional to the square root of the length. 3T = 2π√(L'/g)where L' is the new length of the pendulum.Dividing the second equation by the first equation, we get:basic 3 = √(L'/L)Squaring both sides, we get:basic 9 = L'/LTherefore, the length of the pendulum should be increased by 9 times to increase the time period to 3T.
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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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