A

To keep the block stationary with respect to the wedge, we need to apply Newton's laws to analyze the forces acting on both the block and the wedge.
Step 1: Assume the wedge is accelerating horizontally to the right with an acceleration 'a'. The angle of the wedge with the horizontal is 'θ'.
Step 2: For the block to remain stationary on the wedge, the net acceleration of the block must equal the acceleration of the wedge. Thus, we set up the equations based on the components of the forces.
The force acting down the slope on the block due to gravity is given by:
$$ F_{gravity} = mg o { mg ext{ is the weight of the block} } $$
The acceleration along the incline due to the wedge's motion will be:
$$ a = g an(θ) $$
Step 3: Now, equating the needed force components, we deduce that for the wedge to provide this acceleration 'a', the horizontal force must counterbalance the gravitational component:
$$ F_{horizontal} = m imes a = mg an(θ) $$
Therefore, the wedge should be given a horizontal acceleration towards the left with a magnitude equal to $$ a = g an(θ) $$, and the force applied on the wedge would be $ F_{horizontal} = mg an(θ) $. Hence, A.