Question

A pendulum oscillates simple harmonically and only if
(I) the sizer of the bob of pendulum is negligible in comparison with the length of the pendulum
(II) the angular amplitude is less than 10°.

• A. Both (I) and (II) are correct
• B. Both (I) and (II) are incorrect
• C. Only (I) is correct
• D. Only (II) is correct

Answer 1

The Correct Option is A

For a pendulum to oscillate with simple harmonic motion (SHM), the restoring force must be directly proportional to the displacement and directed towards the mean position. This condition is satisfied when the following conditions are met:

(I) the size of the bob of pendulum is negligible in comparison with the length of the pendulum: This is correct. If the bob's size is comparable to the pendulum's length, the moment of inertia of the system becomes more complex, and the restoring force is no longer directly proportional to the displacement.

(II) the angular amplitude is less than 10°: This is correct. For small angles, the sine of the angle is approximately equal to the angle itself (in radians). This approximation is crucial for the simple harmonic motion equation to hold true. For larger angles, the approximation breaks down, and the motion is no longer simple harmonic.

The correct answer is (A) Both (I) and (II) are correct.