A simple pendulum is suspended from the ceiling of an elevator. When the elevator accelerates upwards with an acceleration of g 3 , the time period of oscillation is T₁ . When the elevator accelerates downwards with an acceleration of g 2 , the time period is T₂ . The ratio T₁ T₂ is:

Step-by-step solution

The time period of a simple pendulum in an accelerating frame is given by T = 2 l g_ eff . For upward acceleration a₁ = g 3 , the effective acceleration due to gravity is: g_ eff 1 = g + g 3 = 4g 3 For downward acceleration a₂ = g 2 , the effective acceleration due to gravity is: g_ eff 2 = g - g 2 = g 2 The ratio of the time periods is: T₁ T₂ = g_ eff 2 g_ eff 1 = g/2 4g/3 = 3 8 . Answer: 3 8