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The question is: If length of the pendulum is halved time period will be?

Correct answer: A. T/sq root 2

  • A. T/sq root 2
  • B. T/2
  • C. T/3
  • D. T/4

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 the length of the pendulum is halved, the new length becomes L/2. Let's denote the new time period as T'.T' = 2π√((L/2)/g)T' = 2π√(L/2g)T' = √(1/2) * 2π√(L/g)T' = (1/√2) * TT' = T/√2Therefore, the new time period (T') is T/√2, which is the same as T divided by the square root of 2.

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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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