1. Tardigrade
  2. Question
  3. Physics
  4. 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)

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Q. 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)

NTA AbhyasNTA Abhyas 2022

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.
Solution
Balancing force,
$F=2\mu N$ …….(i)
Balancing torque (about right side corner):
$Fx+Na=\mu N\left(\right.2x+l\left.\right)$ ……..(ii)
Solving gives,
$\mu =\frac{a}{l}$