Question

Block of mass m kept on smooth incline of a wedge of mass m. find minimum force f such that block leaves the surface

Answer 1

Please find the solution in the attachment.

Answer 2

Answer: Minimum force $F_{min} = mg cot \theta$

Given:

Mass: m

Force: f

Solution:

Taking the wedge as the reference frame.

A force acts on the wedge which is on a smooth horizontal surface.

Therefore, the force will accelerate the wedge.

Thus, the force is given by:

       F = ma,

               Where, a is the acceleration.

On resolving the force equilibrium,

       $mg cos \theta = n + ma sin \theta$

When the block leaves the inclined surface, the normal force becomes zero

       $mg cos \theta = ma sin \theta$

      $g cos \theta = F_{min}/m sin\theta$

      $F_{min} = mg cot \theta$