A simple pendulum is suspended from the ceiling of trolley which is sliding down on a inclined plane of inclination theta. Find the angle made by the string with trolley (a) when trolley slides down with uniform velocity (b) when the plane is smooth.

A simple pendulum is suspended from the ceiling of trolley which is sl

1.	A simple pendulum is suspended from the ceiling of trolley which is sliding down on a inclined plane of inclination theta. Find the angle made by the string with trolley (a) when trolley slides down with uniform velocity (b) when the plane is smooth.
Answer» Solution :(a) Let T be the tension in the string and the string makes an angle `ALPHA` with the normal to the trolley. In equilibrium, `T cos alpha = Mg cos theta` `T sin alpha = Mg sin theta` `TAN alpha = Tan theta rArr alpha = theta` (b) When trolley is SLIDING on smooth INCLINED plane, the acceleration trolley `a = g sin theta`. The bob of the pendulum experiences a PSEUDO force .ma. opposite to the acceleration of the trolley. In equilibrium, `T sin alpha + Ma = Mg sin theta` `T sin alpha = Mg sin theta - Ma = Mg sin theta - Mg sin theta` `T sin alpha = 0 rArr sin alpha = 0 rArr alpha = 0`