A simple pendulum has a time period T₀ when oscillating in a stationary elevator in air. The pendulum is then suspended from the ceiling of an elevator that is accelerating upwards with an acceleration g . The pendulum bob is completely immersed in a non-viscous liquid whose density is half the density of the material of the bob. The new time period of the pendulum will be

Step-by-step solution

The time period of the pendulum in a stationary elevator in air is: T₀ = 2 l g When the elevator accelerates upwards with acceleration a = g , the apparent acceleration due to gravity in the non-inertial frame of the elevator is: g_ app = g + a = g + g = 2g When the bob is immersed in a liquid, the buoyant force acts opposite to the apparent gravity. The effective acceleration due to gravity g_ eff is given by: g_ eff = g_ app (1 - _L _S ) where _L is the density of the liquid and _S is the density of the bob. Give