A block is kept on a frictionless inclined su | vedclass

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(B) Let the mass of the block be $m$. To keep the block stationary relative to the inclined surface, we analyze the forces in the non-inertial frame o

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$g 	an \alpha$

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(B) Let the mass of the block be $m$. To keep the block stationary relative to the inclined surface, we analyze the forces in the non-inertial frame of the incline.$1$. The forces acting on the block are its weight $(mg)$ acting downwards, the normal force $(N)$ perpendicular to the surface, and the pseudo force $(ma)$ acting horizontally in the direction opposite to the acceleration of the incline.$2$. Resolving the forces along the inclined surface:- The component of the gravitational force down the incline is $mg \sin \alpha$.- The component of the pseudo force up the incline is $ma \cos \alpha$.$3$. For the block to remain stationary relative to the incline, these two forces must balance each other:$ma \cos \alpha = mg \sin \alpha$$4$. Dividing both sides by $m \cos \alpha$:$a = g \frac{\sin \alpha}{\cos \alpha}$$a = g 	an \alpha$

$A$ block is kept on a frictionless inclined surface with an angle of inclination '$\alpha$'. The incline is given a horizontal acceleration '$a$' to keep the block stationary relative to the incline. Then '$a$' is equal to:

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