Home Physics Simple Harmonic Motion (Oscillations) Simple Pendulum Which of the following statements is not tru…
Physics Simple Harmonic Motion (Oscillations) Simple Pendulum Single Correct MCQ
Published on: September 11, 2026

Which of the following statements is not true? In the case of a simple pendulum for small amplitudes the period of oscillation is

A
Directly proportional to square root of the length of the pendulum
B
Inversely proportional to the square root of the acceleration due to gravity
C
Dependent on the mass, size and material of the bob
D
Independent of the amplitude

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Text Solution

Verified by Experts
The correct answer is:
C
In a simple pendulum, the period of oscillation $T$ can be described by the formula:
$$T = 2\pi \sqrt{\frac{L}{g}}$$
where $T$ is the period, $L$ is the length of the pendulum, and $g$ is the acceleration due to gravity.
Now, let's analyze each statement:

Option A: Directly proportional to square root of the length of the pendulum.
This is true as $T \propto \sqrt{L}$.

Option B: Inversely proportional to the square root of the acceleration due to gravity.
This is also true as $T \propto \frac{1}{\sqrt{g}}$.

Option C: Dependent on the mass, size, and material of the bob.
This statement is not true as the mass and material of the bob do not affect the period of a simple pendulum (for small amplitudes).

Option D: Independent of the amplitude.
This is true for small amplitudes, where the small angle approximation holds.

Therefore, the statement that is not true is Option C.

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