The time period of a simple pendulum -having a spherical wooden bob is 2 second. If the bob is replaced by a metallic one twice as heavy, the time period will be—

The time period of a simple pendulum is governed by the formula T = 2π√(L/g), where L represents the length of the pendulum and g is the acceleration due to gravity. This mathematical relationship demonstrates that the period is solely dependent on the length of the string and the local gravitational field, making it completely independent of the mass or material of the bob [1]. Whether the bob is made of wood or a metal twice as heavy, the mass factor cancels out during the derivation of the motion equations. Consequently, replacing a wooden bob with a metallic one of different mass does not alter the time taken for one oscillation [1]. Since the initial time period was 2 seconds, it will remain 2 seconds regardless of the change in the bob's mass.

Sources

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