Question

A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then a is equal to

(a) g

(b) gtanα

(c) g/tanα

(d) gcosecα

Answer 1

(b) : The incline is given an acceleration a. Acceleration of the block is to the right. Pseudo acceleration a acts on block to the left. Equate resolved parts of a and g along incline.
Therefore,  macosα = mgsinα
or a = gtanα.