Inside a stationary elevator, a simple pendulum has a time period T₀ . In the same elevator, a projectile fired at a certain angle with a given initial speed has a time of flight equal to T₀ . If the elevator now starts accelerating vertically upwards with an acceleration a = g (where g is the acceleration due to gravity), what will be the ratio of the new time period of the pendulum to the new time of flight of the

Step-by-step solution

In a stationary elevator, the effective gravity is g . The time period of the simple pendulum is T_p = 2 l g = T₀ . The time of flight of the projectile is T_f = 2u g = T₀ . When the elevator accelerates upwards with a = g , the effective acceleration due to gravity becomes g_ eff = g + a = 2g . The new time period of the pendulum is T_p' = 2 l 2g = T₀ 2 . The new time of flight of the projectile is T_f' = 2u 2g = T₀ 2 . The ratio of the new time period to the new time of flight is: T_p' T_f' = T₀ / 2 T₀ / 2 = 2 2