The front wall of a drawer in a cabinet is a provider with two symmetrical handles. The distance between the handles is l and the length (i.e. depth) of the drawer is a . The maximum value of the coefficient of friction between drawer and cabinet, for which drawer can be pulled out by applying a force on one handle perpendicular to the face of the drawer is: (Neglect the weight of the drawer)

Step-by-step solution

If a force is applied only on one handle, as shown in figure, the drawer will have a tendency to rotate clockwise. That is, the right and left corners (shown in figure), will press against the side of the cabinet and produce some friction. Balancing force, F = 2 μ N …….(i) Balancing torque (about right side corner): F x + N a = μ N ( 2 x + l ) ……..(ii) Solving gives, μ = a l