# Equilibrium of Rigid Bodies

A rigid body is said to be in static equilibrium if

1. net external force on the body is zero and
2. net external torque on the body is zero.
The torque may be defined about any point.

## Solved Problems from IIT JEE

### Problem from IIT JEE 2005

A block of mass $m$ is at rest under the action of force $F$ against a wall as shown in figure. Which of the following statement is incorrect?
1. $f=mg$, where $f$ is the frictional force.
2. $F=N$, where $N$ is the normal reaction.
3. $F$ will not produce torque about centre of mass.
4. $N$ will not produce torque about centre of mass.

Solution: The forces acting on the block are its weight $mg$, normal reaction $N$, frictional force $f$, and applied force $F$ (see figure).

Let O be the centre of mass and $N$ acts at a distance $x$ below it. In equilibrium, $N=F$ and $f=mg$. The torque about centre of mass shall be zero i.e., \begin{align} \label{bsb:eqn:1} Nx-fa/2=Fx-mga/2=0. \end{align} Above equation gives $x=mga/(2F)$. The distance $x$ shall be less than or equal to $a/2$ for $N$ to act on the block. Thus, $F \geq mg$ for block to be in equilibrium.