If the amplitude of oscillation of a simple pendulum is very small, then iLs 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 codt: given below.

The time period (T) of a simple pendulum for small amplitudes is governed by the formula T = 2π√(L/g). This indicates that the period is directly proportional to the square root of the length (L) and inversely proportional to the square root of the acceleration due to gravity (g) [3]. Scientific experiments, including those by Galileo, established that the time period remains constant for a given length regardless of the mass of the bob [1]. Furthermore, under the small-angle approximation (typically less than 15°), the motion is considered simple harmonic, making the period independent of the amplitude (A) [3]. Therefore, the period depends on length and gravity but is independent of mass and amplitude. Statements 1, 2, and 4 are correct, while statement 3 is incorrect as mass does not affect the period [1].

Sources

1. [3] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > KNOW A SCIENTIST > p. 108
2. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > THINK LIKE A SCIENTIST! > p. 110
3. [2] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > In a Nutshell > p. 118