In the adjoining figure a wedge is fixed to an elevator moving upwards with an acceleration `a`. A block of mass `m` is placed over the wedge.Find the acceleration of the block with respect to wedge. Neglect friction

Explanation

Since, acceleration of block w.r.t. wedge ( an accelerating or non-inertial frame of reference) is to be find out.
FBD of block w.r.t . Wedge is shown in fig.

The acceleration would had been g `sin theta` (down the plane) if the lift were stationery or when only weight (i.e.,mg) acts downwards.
Here, downward force is m(g+a)
`therefore` Acceleration of the block ( of course w.r.t. wedge) will be (g+a) `sin theta` down the plane.