PAAVAI ENGINEERING COLLEGE (AUTONOMOUS)

DEPARTMENT OF MECHANICAL ENGINEERING

ME23202-ENGINEERING MECHANICS
QUESTION BANK

PART A

Unit 1

1. State Lame’s theorem.

2. Difference between kinetics and kinematics.
3. Define Newton’s second law of motion.
4. State the necessary and sufficient condition for equilibrium.
5. Enumerate principle of transmissibility.
6. What is a coplanar and non-coplanar force?
7. Difference between mass and weight.
8. State triangle law of forces.
9. Difference between Scalar and vector quantity.
10. Determine the cross product of two forces F1 = 2i -3j + 2k and F2 = 2i - 4k
11. State polygon law of forces.
12. Define laws of mechanics.
13. What is a coplanar concurrent force system?
14. Define statics and dynamics.
15. If P ⃗=2i+4j-7k, Q ⃗=3i-5j+6k. Find (2P X 3Q) ⃗
16. Define free body diagram.
17. Given A = 2i - 3j - k and B = i + 4j - 2k. Find A.B and AxB
18. State parallelogram law of forces.
19. Define Engineering Mechanics & Classify its branches?
20. Two concurrent forces of 12 N & 18 N are acting at an angle of 60°. Find the resultant force.
21. List out the different system of forces.
22. What is collinear force system?
23. Differentiate Kinematics and Kinetics.
24. What is resolution of forces?

Unit 2

1. Differentiate moment and couple.

2. Define Varignon’s theorem.
3. A force vector F = 700i + 1500j is applied to a bolt. Determine the magnitude of the force and angle
if forms with the horizontal.
4. A force vector has the components Fx = 150 N, Fy = -200 N, Fz = 300 N. Determine the magnitude
(F) and angle made by the force with coordinate axis.
5. Define beam & mention its types.
6. Classify the types of supports that are used in beam.
7. Write the conditions for equilibrium of a particle/body.
8. State moment of force.
9. What do you mean by force couple system? Classify it.
10. Define equivalent system of forces.
11. What is support? Write the various types of supports.
 12. Write the necessary and sufficient conditions for equilibrium of rigid bodies in 2 dimensions.
13. List out the common types of loads.
14. Draw the reaction components of roller, hinged supports
15. Distinguish uniformly distributed load and uniformly varying load.
16. A force F= 10i + 8j - 5k N acts at a point A [2,5,6]. What is the moment of the force F about the point
B [3,1,4]?
17. What is resultant force?
18. Define Support.
19. List some types of beams based on support.
20. What is rigid body?
21. What is equilibrium force?
22. When is moment of force zero about a point?
23. Define couple.
24. Write the equation of equilibrium of a rigid body?

Unit 3

1. Identify the centroid of an equilateral triangle of height H and width W

2. Define polar moment of inertia.
3. State parallel axis theorem and perpendicular axis theorem.
4. Define centroid
5. Define centre of gravity.
6. Write the expressions to determine centroid of a composite plane area.
7. Locate the centroid and calculate the moment of inertia about centroidal axes of a semi-circular
lamina of radius 2m.
8. Distinguish between centroid and centre of gravity.
9. Define polar moment of inertia.
10. Write down the expression for finding mass moment of inertia of a cylinder of radius ‘R’ and height
‘h’ about its base.
11. Define radius of gyration.
12. Determine the moment of inertia of circle of diameter 40 mm.
13. Differentiate between ‘Mass moment of inertia’ and ‘Area moment of inertia’.
14. Compare the parallel axis and perpendicular axis theorem.
15. Write the standard formula for the moment of inertia of
• rectangle of dimension b, d
• hollow rectangle of dimension B, b, D, d.
16. If a plane area has an axis of symmetry, show that the centroid of the area must lie on this axis.
17. Locate the centroid and write the moment of inertia about centroidal axes of a semicircular lamina
of radius ‘r’.
18. A semi-circular area having radius of 100 mm is located in the XY plane such that its diameter
coincides with the Y axis. Determine the X-coordinate of the centroid.
19. When will centroid and centre of mass coincide?
20. State perpendicular axis theorem.
21. State Parallel axis theorem.
22. Locate the centroid point for the rectangle with dimensions of 100*20 mm.
23. What are the conditions under which center of gravity of a body becomes as same as centroid?
24. Enlist the methods to determine the center of gravity.
Unit 4

1. Write the equations of motion for a particle moving in a straight line.

2. State D Alembert’s principle.
3. Define Rectilinear and curvilinear motion.
4. A car starts from rest with a constant acceleration of 4m/sec2. Determine the distance travelled in
the 7th second.
5. A stone is dropped from top of the tower. It strikes the ground after 4 seconds. Find the height of
the tower.
6. Define angle of projection.
7. What is work energy principle?
8. Differentiate Kinematics and Kinetics.
9. A stone is dropped from the top of a tower. It strikes the ground after four seconds. Find the height
of the tower.
10. The displacement (S) of a particle moves along a straight line measured in meters and given by the
relation in terms of time (t) taken as below: S = 3t3 + 2t2 + 7t + 3. Determine the velocity after 3
seconds.
11. A ball dropped from the top of a tower reaches the ground in 6 seconds. Calculate the height of the
tower.
12. State the applications of work-energy method.
13. Write the impulse momentum equation.
14. List any two examples for connected bodies.
15. Identify a suitable motion for the following applications.
• A disabled car pulled by a rope
• A motion of a car in a straight road
• A newspaper boy throws a paper
• A batsman hits sixer and the ball touches the ground
16. Write work energy equation of particles.
17. What is meant by relative motion?
18. What is general plane motion? Give some examples.
19. A train running at 80 kmph is brought to halt after 60 seconds. Find the retardation and distance
traveled by the train before it comes to a halt.
20. Find the impulse required to stop the car of mass 1000 kg travelling at 80km/hr.
21. Write down the equation of motion of a particle under gravitation.
22. Define impulsive force.
23. A point P moves along a straight line according to the equation x= 4t3+2t+5, where x is in meters
and t is in secs. Solve the velocity and acceleration at t=3 secs.
24. A stone is projected in space at an angle of 45° to horizontal and at an initial velocity of 10 m/sec.
Write the range of the projectile.

Unit 5

1. Define friction.
2. State Coulomb’s laws of dry friction.
3. What is angle of repose?
4. State the different types of frictions.
5. Define coefficient of friction.
6. Define limiting friction.
7. What is General Plane motion?
 8. A block weighing 40 N is just moved along a horizontal plane by applying a horizontal force of 16 N.
Find the reaction and the co-efficient of friction.
9. Define angle of friction.
10. Compare static coefficient of friction and dynamic coefficient of friction.
11. What is meant by impending motion?
12. When do we say that the motion of a body is impending?
13. A body weighing 250N rest on a rough horizontal plane. Find the friction force generated if the body
is subjected to a horizontal pull F. Coefficient of friction is 0.3.
14. Mention the force system in the case of ladder friction.
15. Mention the conditions of friction.
16. State the equilibrium conditions to be satisfied by a ladder at just start of sliding?
17. State any two important law of dry friction.
18. Compare and contrast Ladder friction and Wedge friction.
19. Define rolling resistance.
20. Classify the type of friction.

PART B

Unit 1

1. The four coplanar forces are acting at a point as shown in figure. Determine the resultant in
magnitude and direction.

2. The forces 10 N, 20 N, 30 N and 40 N are acting on one of the vertices of a regular pentagon, towards
the other four vertices taken in order. Find the magnitude and direction of the resultant force R.
3. Find the magnitude of the two forces, such that if they act at right angles, their resultant is √10 N.
But if they act at 60° their resultant is √13 N.
4. The lines of action of three forces are concurrent at the origin 'O', passes through points A,B and C
having coordinates, (3, 0, -3), (2, -2, 4) and (-1, 2, 4) respectively. If the magnitude of the forces are
10 N, 30 N and 40 N, find the magnitude and direction of their resultant.
5. A smooth sphere of weight W is supported by a string fastened to a point A on the smooth vertical
wall, the other end is in contact with point B on the wall as shown in fig. If the length of the string
AC is equal to the radius of the sphere, find the tension in the string and reaction of the wall.
6. The resultant of the force system shown in figure is 520 N along the negative direction of y axis.
Determine P and θ.

7. The tension in cables AB and AC are 100 N and 120 N respectively in figure. Determine the
magnitude of the resultant force acting at A.

8. A cylindrical roller has a weight of 10 KN and it is being pulled by a force which is inclined at 30 with
the horizontal as shown in fig. while moving it comes across an obstacle 10 cm high. Calculate force
required to cross the obstacle if the diameter of roller is 1m.

9. A force F has the components Fx = 150 N, Fy = -200 N, Fz = 300 N. Determine its magnitude of F and
angle made by F with three coordinates.
10. A string ABCD attached to two fixed points A & D has two equal weights of 1000 N attached to it
at B & C, The weights rest with portion AB & CD inclined at angle of 30° & 60° respectively to the
vertical shown in fig. Find the tension in the portions AB, BC & CD of the string, if the inclination of
the portion BC with the vertical is 120°.

11. An electric fixture weighing 10 N hangs from a point O by two strings AO and BO. AO is inclined at
an angle of 600 to the horizontal ceiling and BO is inclined at 450 to the vertical wall as shown in
Fig. Find the forces in the strings AO and BO.
 12. Three smooth pipes each weighing 20 KN and of diameter 60 cm are to be placed in rectangular
channel with horizontal base shown in figure. Calculate the reactions at the points of contact
between the channel and pipes. Take width of channel as 160 cm.

Unit 2

1. ABCD is weightless rod under the action of four forces P, Q, S and T shown. If P = 10 N, Q = 4 N, S =
8 N, T = 12 N. Calculate the resultant and mark the same in direction with respect to end A of the
rod.

2. A system of parallel forces are acting on a rigid bar shown. Reduce the system into
a) A single force.
b) A single force and couple at A.
c) A single force and couple at B.

3. Find the reaction at the supports A & B shown in figure.

4. Determine the support reactions of the beam shown in figure.

5. Four forces of magnitude and direction action on a square ABCD of side 2m are shown. Calculate
the resultant in magnitude & direction. Also locate its point of application with respect to AB &
AD.

6. Find the reaction at the supports of the beam shown in figure.

7. Blocks A & B of weight 200 N and 100 N respectively, rest on a 30˚ inclined plane and are attached
to the post which is held perpendicular to the plane by force P, parallel to the plane as shown in
figure. Assume that all surfaces are smooth and that the cords are parallel to the plane. Determine
the value of P. Also find the normal reaction of blocks A & B.
8. Find the support reactions at A and B of the simply supported beam shown in Fig.

9. Determine the horizontal and vertical components of reaction at the supports. Neglect the
thickness of the beam.

10. Find the reactions at the supports A and B of the beam shown below.

11. Calculate the reactions R1, R2, R3 for two beam AB and CD supported as shown in figure. There
being a hinged connection B and C.
 Unit 3
1. Find the moment of inertia of an unsymmetrical I section shown in figure about its centroidal axes.

2. Find the moment of inertia of the section shown in the figure about its horizontal centroidal axis.

3. Locate the centroid of the hatched area, shown in the figure.

4. Locate the centroid for the plane surface shown below.

5. Evaluate the moment of inertia of shape shown below about an axes passing through its centroid.
6. Determine the Polar Moment of Inertia of symmetrical T section shown in Fig. about its centroidal
axes.

7. Locate the horizontal and vertical centroidal axis for the section shown in figure.

8. Find the moment of inertia of the section shown in figure about the x and y centroidal axes. All
dimensions are in mm.

9. From a rectangular lamina ABCD 10 cm x 12 cm a rectangular hole of 3 cm x 4 cm is cut as shown

in Fig. 6. Calculate the Centroid of the remainder lamina.
10. For the plane area shown in the following figure. Locate the centroid of the area about XX axis.

11. Find the moment of inertia for the below given figure.

12. Locate the centroid of the lamina as shown in the figure.

13. Find the moment of inertia of a channel section as shown in the figure.
 14. Estimate the centroid for the given composite section.

15. Find the moment of inertia of an angle section shown in Fig about its centroidal axes.

Unit 4

1. A stone is dropped from the top of the tower, reaches the ground in 8 seconds, find (i) the height
of the tower (ii) velocity of the particle, when it reaches the ground.
2. A stone is projected upwards from the roof of a building with a velocity of 19.6m/s and another
stone is thrown downwards from the same point, three seconds later. If both the stones reach the
ground at the same time, determine the height of the building. Take g-9.8m/s.
3. A particle moves along a straight line with variable acceleration. If the displacement is measures in
m, and given by the relation in terms of time taken t, as below. S=3t³+2t²+7t+3. Determine (i) the
velocity of the particle at start and after 3 seconds (ii) the acceleration of the particle at start and
after 3 seconds.
4. A particle is projected in air with a velocity 100 m/s and at an angle of 30° with the horizontal, Find
(i) the horizontal range (ii) the maximum height reached by the particle and (iii) the time of flight.
5. The position particle is given by the relation S=9t2+22.5t + 60, where S is expressed in meters and t
in seconds. - Determine
(i) the time at which the velocity will be zero
(ii) the position and distance travelled by the particle at that time
(iii) the acceleration of the particle at that time and
(iv) the distance travelled by the particle from t = 5s to t = 7s.
6. Two bodies of weight 20N and 10N are connected to the two ends of light inextensible string,
passing over a smooth pulley. The weight of 20N is placed on a horizontal surface which the weight
of 10N is hanging free in air as shown in figure. The horizontal surface is a rough one, having co
efficient between the weight 20N and the plane surface equal to 0.3. Using Newton's second law
of motion, determine 1. Acceleration of the system, 2. The tension in the string.

7. A train is traveling from A to D along the track shown in fig. Its initial velocity at A is zero. The train
takes 5 min to cover the distance AB, 2250 m length and 2.5 minutes to cover, the distance BC,
3000 m in length, on reaching the station C, the brakes are applied and the train stops 2250 m
beyond, at D (i) Find the retardation on CD, (ii) the time it takes the train to get from A to D, and
(iii) its average speed for the whole distance.
8. Two weights 80 N and 20 N are connected by a thread and move along a rough horizontal plane
under the action of a force 40 N, applied to the first weight of 80 N as shown in figure. The
coefficient of friction between the sliding surfaces of the wrights and the plane is 0.3. Determine
the acceleration of the weights and the tension in the thread using work-energy equation.

9. A body of mass 15kg is initially at rest on a 100 inclined plane. Then it slides down. Calculate the
distance moved by the body, on the inclined plane, when the velocity reaches to 6 m/s. The
coefficient of friction between the body and the plane is 0.1.
10. A 25 Kg body is projected up a 300 inclined plane with initial speed of 6 m/sec. If the coefficient of
friction is 0.25, determine the time required for the body to have an upward speed of 3 m/sec.
11. Two trains A and B leave the same station on parallel lines. A starts with a uniform acceleration of
0.15 m/s2 and attains the speed of 24 km/hour after which its speed remains constant. B leaves 40
seconds later with uniform acceleration of 0.30 m/s2 to attain a maximum of 48 km/hour, its speed
also becomes constant thereafter. When will B overtakes A?
12. A block and pulley system is shown in figure. The coefficient of kinetic friction between the block
and the plane is 0.25. The pulley is frictionless. Find the acceleration of the blocks and the tension
in the string when the system is just released. Also find the time required for 200 kg block to come
down by 2 m.
 13. A train starts from rest and attains a velocity of 45 km per hour in 2 minutes, with uniform
acceleration. Determine (A) acceleration (B) distance travelled in this time, 2 min. A motorist is
travelling at a speed of 60 km per hour on a curved road of radius 150 m. Calculate the normal
and tangential components of acceleration. Also find the normal and tangential components of
deceleration just after the brakes are applied to slow down his motor uniformly to a speed of 30
km per hour in 10 seconds.
Unit 5

1. Block (2) rests on block (1) and is attached by a horizontal rope AB to the wall as shown in figure.
What force P is necessary to cause motion of block (1) to impend? The coefficient of friction
between the blocks is 1/4 and between the floor and block is 1/3. Mass of blocks (1) and (2) are
14Kg and 9Kg respectively.

2. A uniform ladder of weight 1000N and of length 4m rests on a horizontal ground and leans against
a smooth wall. The ladder makes an angle of 60˚ with horizontal. When a man of weight 750N
stands on the ladder at a distance 3m from the top of the ladder, the ladder is at the point of sliding.
Determine the coefficient of friction between the ladder and the floor.
3. A 7 m long ladder rests against a vertical wall, with which it makes an angle of 45˚ and on a floor. If
a man whose weight is one half that of the ladder climbs it, at what distance along the ladder will
he be when the ladder is about to slip? Take coefficient of friction between the ladder and the wall
is 1/3 and that between the ladder and floor is ½.
4. What should be the value of the angle θ so that motion of the 390 N block impends down the
plane as shown in figure? The coefficient of friction µ for all surfaces is 1/3.
5. Determine the smallest force P required to move the block B shown in Fig. Below, if
A) Block A is restrained by cable CD, and
B) Cable CD is removed. Take μs=0.30 and μk =0.25

6. A block weighing 36 N is resting on a rough inclined plane having an inclination of 30º. A force of
12 N is applied at an angle of 10º up the plane and the block is just on the point of moving down
the plane. Determine the coefficient of friction.
7. A man can pull horizontally with a force of 450 N. A mass of 350 kg is resting on a horizontal surface
for which the coefficient of friction is 0.20. The vertical cable of a crane is attached to the top of the
block as shown in Fig. What will be the tension in the cable if the man is just able to start the block
to the right?

8. A block of 100 kg mass is to be pulled to the right by a horizontal force P as shown in figure. Over
the block another block of 50 kg mass is placed which is attached to the wall by a string. If the
coefficient of friction between all the surfaces is 0.25, determine the value of P, for which motion
is impending. Also, determine the tension in the string connecting the upper block with the wall.

9. A Body of weight 100N is placed on a rough horizontal plane and pushed by a force of 45N as shown
in figure. To just sliding over the horizontal plane. Determine the co-efficient of friction in all three
cases.