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.

More Solved Problems on Equilibrium of Rigid Bodies

• A uniform cube of side a and mass m rest on a horizontal table (IIT JEE 1984)
• A rod of weight W is supported by two parallel knife edges A and B (IIT JEE 1997)
• A cubical block of side L rests on a horizontal surface (IIT JEE 2000)
• Two identical ladders each of mass M and length L are resting (IIT JEE 2005)
• A block of base 10 cm by 10 cm on inclined plane - sliding and toppling (IIT JEE 2009)
• In the figure a ladder of mass m is shown leaning against a wall (IIT JEE 2014)
• A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner (IIT JEE 2016)
• In a physical balance working on the principle of moment balance (JEE Mains 2017)
• A uniform rod AB is suspended from a point X (JEE Mains 2018)

Related Topics

• Kinematics of Rigid Bodies
• Moment of Inertia
• Angular Momentum
• Angular Momentum of a Projectile
• Torque
• Conservation of Angular Momentum
• Fixed Axis of Rotation
• Rolling without slipping of rings cylinders and spheres
• Equilibrium of rigid bodies
• Direction of frictional force on bicycle wheels

References

1. IIT JEE Physics by Jitender Singh and Shraddhesh Chaturvedi
2. 300 Solved Problems on Rotational Mechanics by Jitender Singh and Shraddhesh Chaturvedi