The time period of oscillation of a simple pendulum having length L and mass of the bob m is given as T. If the length of the pendulum is increased to 4L and the mass of the bob is increased to 2m, then which one of the following is the new time period of oscillation?

The time period (T) of a simple pendulum is governed by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. Crucially, the time period depends solely on the length of the pendulum and the local gravity; it is independent of the mass of the bob [1]. According to the formula, the time period is directly proportional to the square root of the length (T ∝ √L) [1]. If the length is increased from L to 4L, the new time period T' becomes 2π√(4L/g). Since √4 equals 2, the new period is 2 × 2π√(L/g), which simplifies to 2T. The increase in mass from m to 2m has no effect on the oscillation period [1]. Therefore, quadrupling the length results in doubling the time period.

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > THINK LIKE A SCIENTIST! > p. 110