If the length of a simple pendulum is being increased by 4-flod, time period of oscillation will be

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 [1]. This relationship indicates that the time period is directly proportional to the square root of the pendulum's length (T ∝ ∐L). When the length of the pendulum is increased by 4-fold (L' = 4L), the new time period T' becomes 2π√(4L/g). Mathematically, this simplifies to 2 × 2π√(L/g), which is exactly twice the initial time period (T' = 2T). Therefore, quadrupling the length results in the time period increasing by a factor of 2 [1]. Other factors, such as the mass of the bob, do not affect the time period [1].

Sources

1. [1] https://carder2.carder.gov.co/case-study/if-the-length-of-a-simple-pendulum-is-quadrupled-4x-increase-its-perio-z8u0ghkf.htm