If the amplitude of oscillation of a simple pendulum is very small, then its time period of oscillation 1. depends on the length of the pendulum, L 2. depends on the acceleration due to gravity, g 3. depends upon the mass of the bob of the pendulum, m 4. does not depend upon the amplitude of the pendulum, A Select the correct answer using the code given below.
- A.1, 2 and 3
- B.1, 2 and 4
- C.2, 3 and 4
- D.1 and 4 only
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Explanation
The correct answer is B, 1, 2 and 4. For small swings the time period is T = 2π√(L/g), which contains the length and gravity but neither the mass nor the amplitude.
Statement 1 is correct: T grows with the square root of length, so a pendulum four times longer takes twice as long per swing. Statement 2 is correct: T falls as g rises, so a pendulum clock runs slow on a hill or on the Moon, where g is smaller. Statement 3 is wrong: the mass of the bob cancels out of the equation, so a heavy and a light bob on equal strings swing together. Statement 4 is correct: for small amplitudes the period is the same however wide the swing, which Galileo noticed and which makes pendulum clocks possible.
A is wrong: it includes statement 3 and leaves out statement 4.
C is wrong: it includes the wrong statement 3 and drops statement 1.
D is wrong: it drops statement 2, though g appears in the formula.
Exam tip: T = 2π√(L/g); independent of mass and (small) amplitude; seconds pendulum ≈ 1 m long, T = 2 s.