A simple pendulum is placed inside a lift, which is moving with a uniform acceleration. If the time periods of the pendulum while the lift is moving upwards and downwards are in the ratio 1: 2 , then the acceleration of the lift is (Acceleration due to gravity, g=10 ~ms ⁻² )

Step-by-step solution

Given, time period of the pendulum while the lift is moving upwards and downward are in the ratio, T₁: T₂=1: 2 Acceleration due to gravity, g=10 ~m / s ^2 We know that, If the lift is moving upward, then total time-period, when the lift is moving downwards, then the total time period, By dividing Eq. (i) to (ii), we get array rlrl & T₁ T₂ & = g-a g+a & Now, & 1 2 & = g-a g+a array Square on the both sides, we get aligned & or & ( 1 2 )^2 & = g-a g+a or g-a g+a = 1 4 & or & 4 g-4 a & =g+a or 3 g=5 a & or & a & = 3 g