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.

Explanation

(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`