The time period of oscillation of a simple pendulum having length L an

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?

T
2T
4T
T/2
This question was previously asked in
UPSC NDA-2 – 2018
The new time period of oscillation is 2T.
The time period (T) of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. The mass of the bob (m) does not affect the time period of a simple pendulum.
Let the initial time period be T₁ = T, with length L₁ = L and mass m₁ = m. The formula is T₁ = 2π√(L/g).
When the length is increased to L₂ = 4L and the mass is increased to m₂ = 2m, the new time period T₂ is calculated using the formula, considering only the change in length:
T₂ = 2π√(L₂/g) = 2π√((4L)/g) = 2π * √4 * √(L/g) = 2π * 2 * √(L/g) = 2 * (2π√(L/g)).
Since T₁ = 2π√(L/g), the new time period T₂ = 2 * T₁. Thus, the new time period is 2T.