A simple pendulum having bob of mass m and length of string l has time period of T. If the mass of the bob is doubled and the length of the string is halved, then the time period of this pendulum will be
- A.T
- B.T/√2
- C.2T
- D.√2T
Correct answer
Explanation
The correct answer is B, T/√2. The time period of a simple pendulum depends on its length but not on the mass of the bob, so halving the length divides the period by √2.
For small swings, the time period of a simple pendulum is T = 2π√(l/g), where l is the length and g is the acceleration due to gravity. Mass does not appear in the formula, so doubling the mass changes nothing. Because T varies as the square root of l, making the length half makes the new period 2π√(l/2g), which is T/√2, or about 0.71 T. This is why a pendulum clock is adjusted by moving the bob up or down, and why it runs slow on the Moon, where g is smaller.
A is wrong because the shorter length does change the period. C is wrong because 2T would need the length to be made four times longer. D is wrong because √2T would need the length to be doubled, not halved.
Exam tip: T = 2π√(l/g): independent of mass; four times the length doubles the period.
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