An oscillating pendulum suspended from the roof of a lift which is at rest has time period T₁ . When lift moves up with acceleration 'a' its time period is T₂ . When lift moves down with acceleration 'a' its time period is T₃ . The relation between T₁ , T₂ and T₃ is

Step-by-step solution

The time period of a simple pendulum is given by T = 2 l g_ eff . When the lift is at rest, the effective acceleration due to gravity is g . T₁ = 2 l g 1 T₁^2 = g 4 ^2 l When the lift moves up with acceleration a , the effective acceleration due to gravity is g + a . T₂ = 2 l g+a 1 T₂^2 = g+a 4 ^2 l When the lift moves down with acceleration a , the effective acceleration due to gravity is g - a . T₃ = 2 l g-a 1 T₃^2 = g-a 4 ^2 l Adding the equations for 1 T₂^2 and 1 T₃^2 : 1 T₂^2 + 1 T₃^2 = g+a 4 ^2 l + g-a 4 ^2 l