The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum?
- A.3:1
- B.2:5
- C.2:1
- D.3:2
Correct answer
Explanation
The correct answer is C, 2:1. The time period of a simple pendulum depends on the square root of its length and not on its mass, so four times the length gives twice the period.
For small swings the time period is T = 2π√(L/g), where L is the length of the pendulum and g the acceleration due to gravity. Mass does not appear in the formula, so doubling the bob's mass changes nothing. If L becomes 4L, the new period is 2π√(4L/g) = 2 × 2π√(L/g), that is 2T. The ratio of the new period to the old one is therefore 2:1. The same formula explains why a pendulum clock runs slow on a hill, where g is a little smaller.
A is wrong because a 3:1 ratio would need the length to grow nine times. B is wrong because the period cannot fall when the length rises. D is wrong because 3:2 would need the length to grow 2.25 times.
Exam tip: T ∝ √L, independent of mass; four times the length means double the period.
Practice Questions
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