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

Question

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

Options

G1 Physics · Accepted Answer

Initial time period: T₁ = 10/20 = 0.5 s. For 40 oscillations in the same 10 s, T₂ = 10/40 = 0.25 s. Therefore, T₂/T₁ = 1/2. For a simple pendulum, T ∝ √L. Hence, L₂/L₁ = (T₂/T₁)² = (1/2)² = 1/4. Thus, L₂ = 30/4 = 7.5 cm. Correct option: C.

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