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(D) The correct option is $(d)$.When the block slides down the frictionless inclined plane with an acceleration $a = g \sin \alpha$,we analyze the mot

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perpendicular to the inclined plane $AC$

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(D) The correct option is $(d)$.When the block slides down the frictionless inclined plane with an acceleration $a = g \sin \alpha$,we analyze the motion of the pendulum bob in the non-inertial frame of reference of the block.$(i)$ The forces acting on the pendulum bob in the frame of the block are the gravitational force $mg$ (acting vertically downwards) and the pseudo force $ma = mg \sin \alpha$ (acting upwards parallel to the inclined plane).$(ii)$ The effective acceleration $g_{eff}$ experienced by the bob is the vector sum of the acceleration due to gravity $\vec{g}$ and the pseudo acceleration $-\vec{a}$.$(iii)$ The mean position of the pendulum corresponds to the direction of this effective acceleration $\vec{g}_{eff}$.$(iv)$ By resolving the gravitational force $mg$ into components perpendicular to the plane $(mg \cos \alpha)$ and parallel to the plane $(mg \sin \alpha)$,we see that the parallel component $mg \sin \alpha$ is exactly cancelled by the pseudo force $mg \sin \alpha$ acting in the opposite direction.$(v)$ Thus,the only remaining component of the effective force is $mg \cos \alpha$,which acts perpendicular to the inclined plane $AC$. Therefore,the string of the pendulum aligns itself perpendicular to the inclined plane at its mean position.

$A$ simple pendulum is attached to a block which slides without friction down an inclined plane $ABC$ 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

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