A simple pendulum of string length 30 cm performs 20 oscillations in 10 s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is _ _ _ _ cm. [Assume that the mass of the pendulum remains same.]

Step-by-step solution

Period of simple pendulum: T = time number of oscillations Initial period: T₁ = 10 20 = 0.5 s Required period: T₂ = 10 40 = 0.25 s Using T = 2 L g , the ratio is: T₂ T₁ = L₂ L₁ 0.25 0.5 = L₂ 30 0.5 = L₂ 30 0.25 = L₂ 30 L₂ = 7.5 cm