The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum ?

The time period (T) of a simple pendulum is governed by the formula T = 2π√(L/g), where L is the length and g is the acceleration due to gravity. Crucially, the time period is independent of the mass of the bob [1]. Therefore, doubling the mass has no effect on the period. When the length (L) is increased four times (L' = 4L), the new time period T' becomes 2π√(4L/g). Since √(4L) = 2√L, the new period T' is exactly twice the original period T (T' = 2T). Consequently, the ratio of the new time period to the previous time period is 2:1. This relationship demonstrates that the period is directly proportional to the square root of the length.

Sources

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