A smooth inclined plane of angle of inclination 30 degree is placed on the floor of a compartment of a train moving with constant acceleration a When a block is placed on the inclined plane it do not slide down or up the plane The acceleration a must be
​a. g b. g/2 c. g/(root 2) d. g/(root 3)

See this is a case of non inertial frame of reference. Here, in addition to gravity, an additional accelaration acts on the body backwards known as pseudo force due to which the body doesn’t fall. There is no friction therefore the accelaration down the slope for the body = gsin30 is balanced by the accelaration due to pseudo force upwards = asin(90-30) = acos 30, putting the values we get a = g / root 3