A simple pendulum oscillating in air has a period of 3 second. If it is immersed in a non-viscous liquid, having density = ( 1 x ) , where is the density of the material of the bob, the new period is 2 second. The value of x is

Step-by-step solution

The time period of a simple pendulum in air is given by: T₁ = 2 L g = 3 When immersed in a liquid, the effective acceleration due to gravity becomes: g_ eff = g (1 - ) The new time period is: T₂ = 2 L g_ eff = 2 Taking the ratio of the two time periods: T₂ T₁ = g g_ eff = 1 1 - Substituting the given values T₁ = 3 , T₂ = 2 , and = x : 2 3 = 1 1 - 1 x Squaring both sides: 4 3 = 1 1 - 1 x 1 - 1 x = 3 4 1 x = 1 - 3 4 = 1 4 x = 4 Answer: 4