Multiple choice

The length of a simple pendulum is increased by 44%. What is the percentage increase in its time period?

  1. 20%

  2. 30%

  3. 40%

  4. 50%
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A Correct answer
Explanation

T = 2 * pi * sqrt(L/g). If L increases by 44%, L_new = 1.44 * L. T_new = 2 * pi * sqrt(1.44 * L / g) = 1.2 * T. The increase is 20%.

AI explanation

The time period of a simple pendulum is directly proportional to the square root of its length, meaning the time period becomes the square root of the new length percentage. Increasing the length by 44% makes the new length 144% of the original, so the new time period is the square root of 144, which is 120%. The time period increases from 100% to 120%, resulting in a 20% increase.

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