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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 normal to the trolley (a) when trolley slides down with uniform velocity (b) when the plane is smooth. |
Answer» Solution :(a) Let T be 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` |
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