A pendulum clock is lifted to a height where the gravitational acceleration has a certain value g. Another pendulum clock of the same length but of double the mass of the bob is lifted to another height where the gravitational acceleration is g/ 2. The time period of the second pendulum would be in terms of period T of the first pendulum

The time period of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length and g is the acceleration due to gravity. Crucially, the period is completely independent of the mass of the bob [1]. In the first scenario, the period is T = 2π√(L/g). In the second scenario, although the mass is doubled, this change does not affect the period [1]. However, the gravitational acceleration is reduced to g/2. Substituting this into the formula, the new period T' = 2π√(L/(g/2)) = 2π√(2L/g). This can be rewritten as T' = √2 * (2π√(L/g)). Since the term in the parentheses is the original period T, the new period is √2 T. Therefore, the second pendulum's period is √2 times the first.

Sources

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