1. Assignment No. 2
EQUILIBRIUM OF RIGID BODIES or EQUILIBRIUM
PART I
1. Define and explain the term ‘Equilibrium’. What do you understand by ‘Equilibrant’?
2. State and explain ‘Principles of Equilibrium’ or ‘Equilibrium law’.
3. What are the different conditions of equilibrium?
4. What are the different conditions of equilibrium for:
A) Non-concurrent Force System
B) Concurrent Force System
5. What do you understand by ‘Free Body’ and ‘Free Body Diagram’? What is the
application of Free Body Diagram?
6. State ‘Lami’s Theorem’.
7. Draw the Free Body Diagram for following System:
Figure 1 Figure 2
Figure 3 Figure 4

2. Figure 4 Figure 5
Figure 6 Figure 7
Figure 6 Figure 7

3. 8. A pulley of 2 m diameter is subjected to coplanar forces as shown in following figure.
Is pulley in equilibrium? If not what should be done to keep it in equilibrium?
9. A pulley of 3 m diameter is subjected to coplanar forces as shown in following figure.
Is pulley in equilibrium? If not what should be done to keep it in equilibrium?
10. A spheres of weight 50 kN and of radius 10 cm rest in a channel as shown in
following Fig. Find the reactions at point of contacts. Assume all the surfaces to be
smooth.

4. 11. A spheres of weight 50 kN and of radius 10 cm rest in a channel as shown in above
Fig. Find the reactions at point of contacts. Assume all the surfaces to be smooth.
12. Two identical rollers, each of weight 500 N, are supported by an inclined plane and a
vertical wall as shown in Fig. below. Find the reactions at point of contacts A, B and
C. Assume all the surfaces to be smooth.
13. Two rollers, each of weight 1000 N and 500 N, are supported by an inclined plane and
a vertical wall as shown in Fig. below. Find the reactions at point of contacts A, B and
C. Assume all the surfaces to be smooth.
14. Two identical rollers, each of weight 1000 N and 500 mm in diameter are supported
by an inclined plane and a vertical wall as shown in Fig. below. Find the reactions at
point of contacts A, B and C. Assume all the surfaces to be smooth.
15. Two rollers, each of weight 1000 N and 500 N, are supported by an inclined plane and
a vertical wall as shown in Fig. below. Find the reactions at point of contacts A, B and
C. Assume all the surfaces to be smooth.

5. 16. Two spheres each of weight 1000 N and of radius 25 cm rest in a horizontal channel
of width 90 cm as shown in following Fig. Find the reactions at point of contact.
Assume all the surfaces to be smooth.
17. Two cylinders A and B, of weight 1000 N and 500 N respectively, are supported by
inclined plane and a vertical wall as shown in Fig. below. The radius cylinders A and
B are 250 mm and 157 mm respectively. Find the reactions at point of contacts.
Assume all the surfaces to be smooth.
18. Two cylinders 2 and 1, of weights 1000 N and 500 N respectively, are supported by
inclined planes as shown in Fig. below. The radius cylinders 2 and 1 are 150 mm and
100 mm respectively. Find the reactions at point of contacts. Assume all the surfaces
to be smooth.

6. MISCELLANEOUS PROBLEM
19. A 500 N cylinder, 1 m diameter, is loaded between the cross pieces which make an
angle of 600 with each other and are pinned at C. Determine the tension in the
horizontal rope DE assuming a smooth floor. Refer Figure 1.
Fig. 1
20. Two cylinders A and B are connected by a rigid bar of negligible weight hinged to
each cylinders and are left to rest in eqm in a position as shown below under the
application of a force ‘P’ applied at the centre of cylinder B. Determine the magnitude
of force P if the wt. of each cylinders A and B are 100 N and 50 N resp.

7. PART II
FRICTION
Problems:
Type I
1) A body of weight 150 N is placed on a rough horizontal plane. Determine the co-efficient
of friction when a force of 80 N just causes the body to slide over a horizontal plane.
2) A body of weight 100 N is placed on a rough horizontal plane. If the co-efficient of
friction is 0.3. Determine the horizontal force required to just slide over a horizontal
plane.
3) A force of 15 N is required to pull a body of weight 50 N on a rough horizontal plane.
Find the co-efficient of friction if the applied force makes an angle of 150 with the
horizontal.
4) Solve the same problem if a push of 15 N force makes an angle of 150 with the horizontal.
5) Calculate the angle of friction for problem (1) and (3).
Type II
1) A body of weight 500 N is pulled up on an inclined plane by a force of 350 N. the
inclination of the plane is 300 to the horizontal and the force is applied parallel to the
plane. Determine the co-efficient of friction.
Type III
1) Block B weighs 100 N. Determine the maximum weight of block A for which the system
will be in equilibrium. The co-efficient of friction between block B and table is 0.20.
(Dec. 2009 10 MKS)