A car is moving with a constant speed of 20 m s - 1 in a circular horizontal track of radius 40 m . A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m s - 2 )

Step-by-step solution

Let the frame of reference to be attached to the car with x-axis along horizontal direction and y-axis along vertical direction. Since the frame of reference is a rotating frame, a centrifugal force term should be added while applying Newton's second law. Let θ be the angle made by the pendulum with the vertical. Applying Newton's second law for horizontal direction: T sin θ   - m v 2 R = 0 (since the acceleration of the pendulum in the rotating frame is 0). ∴ T sin θ   = m v