Published by:
CGP EDU Academic Team
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
Text Solution
Verified by ExpertsThe 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.
$$T = 2\pi \sqrt{\frac{L}{g}}$$
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.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The period of a simple pendulum is doubled, when
The period of oscillation of a simple pendulum of constant length at earth surface is T. Its period…
A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means …
A pendulum suspended from the ceiling of a train has a period T, when the train is at rest. When th…
The mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum o…
A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horiz…