Question

The door of an almirah is $4m$ high, $1m$ wide and weights $50kg$. The door is supported by two hinges situated at a distance of $1.0m$ from the ends. If the magnitude of each forces exerted by the hinges on the door is equal, find this magnitude.

Answer 1

the free-body diagram of the door is shown in figure. The forces exerted on the hinges are equal in magnitude. The door is in equilibrium in horizontal as well as in vertical direction, i.e., the horizontal and vertical components of the forces will be equal.
For the vertical equilibrium of the door, we have
$\sum F_v=0;2F_v=500\Rightarrow F_v=250N$
For rotational equilibrium of the door, we have $\sum {\tau }^{}=0$
Taking moment of all forces acting on the door about lower hinge (may be upper hinge or any other point), we get
$500\times 1.0-F_H\times =0$ which gives $F_H=250N$
the force on the door exerted by either hinge, in magnitude, is
$F=\sqrt{F_H^2+F_v^2}=\sqrt{{250}^2+{250}^2}=250\sqrt{2}N$