A simple pendulum is suspended from the ceiling of a stationary truck, and its time period of small oscillations is T . If the truck suddenly starts accelerating horizontally with an acceleration of 3 g , the new time period of the pendulum becomes T' . The ratio T' T is:

Step-by-step solution

When the truck is stationary, the time period of the simple pendulum is given by: T = 2 L g When the truck accelerates horizontally with acceleration a = 3 g , the pendulum is in a non-inertial frame. The effective acceleration due to gravity g_ eff is the vector sum of the actual gravity g downwards and the pseudo acceleration a horizontally. g_ eff = g^2 + a^2 g_ eff = g^2 + ( 3 g)^2 = g^2 + 3g^2 = 4g^2 = 2g The new time period T' of the pendulum in the accelerating truck is: T' = 2 L g_ eff = 2 L 2g Taking the r