Question

A block of mass m lies on wedge of mass M as shown in figure.

With what minimum acceleration must the wedge be moved towards right horizontally so that block m falls freely.

Answer 1

g cot θ

Answer 2

For the block to fall freely, the normal force from the wedge must become zero. In the wedge's non-inertial frame, the block experiences gravity mg, normal force N, and a pseudo force ma (opposite to wedge's acceleration). Resolving forces perpendicular to the incline, the outward pseudo force component ma sinθ must balance the inward gravitational force component mg cosθ for N to be zero. This leads to ma sinθ = mg cosθ, resulting in a = g cotθ.