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A simple pendulum is attached to a block which slides without friction down an inclined plane $A B C$ having an angle of inclination $\alpha$ as shown below. While the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string is
at angle $\alpha$ to the perpendicular to the inclined plane $A C$
parallel to the inclined plane $A C$
vertically downwards
perpendicular to the inclined plane $A C$
Solution
(d)
As block slides down the plane, pendulum bob is subjected to two forces.
$(i)$ Weight mg perpendicularly downwards to the horizontal.
$(ii)$ Pesudo force $m g \sin \theta$ acting upwards and parallel to the inclined plane.
Resultant of these forces is perpendicular to inclined plane $A C$. So, mean position of pendulum is perpendicular to $A C$.
