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DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI
DEPARTMENT OF MECHANICAL ENGINEERING
GE 6253 ENGINEERING MECHANICS
UNIT – I : BASICS AND STATICS OF PARTICLES
PART – A (2 MARKS)
1. Define principle of transmissibility of forces
(M-15, N-13, M-12, N-09 )
If a force acts at any point on a rigid body it may also be considered to act at any other point on its line of action
2. State Lami‟s theorem
(M-11)
It states that if three coplanar forces acting at a point be in equilibrium then each force is proportional to the sine of the
angle between the other two.
Mathematically P/Sinα = Q/Sinβ = R/Sinγ
3. Explain parallelogram law of force
(N-09, M-12)
It states that if two forces acting simultaneously at a point be represented in magnitude and direction by the two
adjacent sides of a parallelogram then the resultant of these forces is represented in magnitude and direction by
the diagonal of that parallelogram originating from that point.
Mathematically R =√( P2+Q2+ (2PQCosθ))
4. Explain triangular law of forces
(N-13)
It states that if two forces acting at a point are represented by the two sides of a triangle taken in order then their
resultant force is represented by the third side taken in opposite order.
5. Explain polygon law of forces
(N-14,M-15)
It states that if a number of coplanar forces are represented in magnitude and direction by the sides of a polygon taken
in a order then their resultant force is represented by the closing side of the polygon taken in the opposite order.
6. What is a force?
(M-12)
Force is an agent which changes or tends to change the state of rest or of uniform motion of a body upon which it acts.
A force represents the action of one body on another. Force is a vector quantity.
7. What are the characteristics of a force?
(N-11)
A force is characterized by i). Magnitude ii).line of action iii).direction
8. What are the classification of force system?
(M-07)
A system of force is classified into i).coplanar forces ii).Non coplanar forces or spatial forces
9. What is a coplanar force?
(N-08, M-11)
Coplanar force systems have all the forces acting in one plane. They may be collinear, concurrent, parallel, nonconcurrent or non-parallel.
10. What is a concurrent force?
(N-07)
A concurrent coplanar force system is a system of two or more forces whose lines of action all intersect at a
common point.
11. What is a non coplanar force?
(M-11)
In non coplanar force system the forces do not act in one plane
12. What is a collinear force?
(N-08, M-09)
The force which acts on a common line of action are called collinear forces. If they act in same direction they are called
like collinear and if they act in opposite direction they are called unlike collinear
13. What is a parallel force?
(M-12)
In parallel system line of action of forces are parallel to each other. Parallel forces acting in same direction are called
like parallel forces and the parallel forces acting in opposite direction are called unlike parallel forces.
14. What is the difference between coplanar concurrent force and coplanar non concurrent force?
(M-12, N-14)
Coplanar concurrent force - Forces intersects at a common point and lies in a single plane
Coplanar non concurrent force - Forces which do not intersects at a common point but acts in one plane
15. What is the difference between like collinear coplanar force and unlike collinear coplanar force?
(M-06)
Like collinear coplanar force -Forces acting in same direction, lies on a common line of action and acts in a single
plane
Unlike collinear coplanar force -Forces acting in opposite direction, lies on a common line of action and acts in a single
plane
16. Define - statics
(M-12)
It is defined as the branch of rigid body mechanics, which deals with the behaviour of a body when it is at rest
17. What is the difference between like non coplanar concurrent force and non coplanar non concurrent force?
(N-07, N-11)
Non coplanar concurrent force
Forces intersects at one point but their lines of action do not lie on the same plane
Non coplanar non concurrent force
Forces do not intersects at one point and also their lines of action do not lie on the sameplane
18. What is resultant force?
(N-13)
If a number of forces acting on a particle simultaneously are replaced by a single force, which could produce the same
effect as produced by the given forces, that single force is called Resultant force. It is equivalent force of all the given
forces.
19. Define - Dynamics
(N-12)
It is defined as the branch of rigid body mechanics, which deals with the behaviour of a body when it is in motion.
20. State Newton‟s law of motion
(M-14)
Newton‟s first law: Everybody preserves in its state of rest, or of uniform motion in a straight line unless it is compelled
to change that state by forces impressed there on.
Newton‟s second law: The acceleration of a particle will be proportional to the force and will be in the direction of the
force
Newton‟s third law: To every action there is an equal and opposite reaction.
21. What is equlibrant and equlibrium ?
(N-09, M-15, N-12)
A force E with same magnitude and same line of action but opposite Direction is called equilibrant.
The equilibrant used to arrest the movement of the particle, then the body is said to be in equilibrium. Here Resultant =
0.
22. What are the conditions for equilibrium ?
(N-11,M-13)
For collinear forces, ∑H = 0, ∑V = 0
For concurrent forces, ∑ H = 0 , ∑V = 0
23. Define - Free body & Free body diagram
A body which has been isolated from surroundings is called Free body.
The sketch showing all the forces and moments acting on the Free body is called free body diagram.
(M-15)
PART – B (16 MARKS)
1. A system of forces acting on a body is as shown in fig. Determine the resultant of the force and its direction.
(M-12)
2. Determine the tension in cables AB and AC required to hold the 40kg crate shown
(N-12)
3. Three forces act on a particle „O‟ as shown in fig. Determine the value of „F‟ such that the resultant of these
three forces is horizontal. Find the magnitude and direction of the fourth force which when acting along with the
given three forces will keep „O‟ in equilibrium.
(M-14)
y
30
kN
3
0
°
F
4
01
°0
°
O
18
kN
x
4. Determine the required length of the cord AC in fig, so that the 8kg lamp is suspended in the position shown.
The undeformed length of the spring AB is l‟AB= 0.4m, and the spring has a stiffness of kAB = 300 N/m.
2m
C
30°
300N/m
A
B
(N-11)
5. Members OA, OB and OC form a three member space truss. A weight of 10kN is suspended at the joint O as
shown in fig. Determine the magnitude and nature of forces induced in each of the three members of the truss.
(N-08)
6. A force acts at the origin of a coordinate system in a direction defined by the angles x = 69.3 andz = 57.9.
Knowing that the „y‟ component of the force is –174 N, determine (i) the angle y, (ii) the other components and
the magnitude of the force (iii) the projection of this force on xz plane. And its magnitude and (iv) moment of this
force about the point co ordinate (2, 3, 4) and its magnitude.
(N-12)
7. Determine the reactions at A and B.
(M-11, N-08)
300 mm
dia
A
10
0
N
6
0

we
igh
t
B
4
5

8. A 90 N load is suspended from the hook and supported by two cables shown in fig. Determine the forces in the
cables for equilibrium. Cable AD lies in the x-y plane and cable AC lies in the x-z plane.
C
z
3
5
4
3
0

D
B
A
x
9
0
N
y
(N-06)
9. A container is supported by three cables as shown. Determine the weight W of the container, knowing that the
tension cable AB is 500N.
(M-12)
y
3
0 D
30
8z
0
C
O
A
3
2
2
B 0
3x
0
4
8
0
10. Determine the magnitude and direction angles of force F in the figure that are required for equilibrium of particle
at O.
(M-15)
6
2
F3 =
B 700
N
z
y
m
m
F
O
F1 =
400
F2 =
800 N
3
m x
N as shown in figure. Determine the forces in each cord for
11. The 50 kg pipe is supported by a system of five cords
equilibrium.
(M-14)
5 3
4
C
D
B
6
0

A
E
5
0
12. Two cylinders of diameters 60mm and 30mm wighing
k 160 N and 40 N respectively are placed as shown in fig.
g
Assuming all contact surfaces to be smooth find the Reactions at all the contact surfaces.
72
mm
D
C
A
4
5  60
 mm
B

30
(N-11)
13. Determine the stretch in each spring for equilibrium of the weight W = 40 N block as shown in Fig. The springs
are in equilibrium position. The stiffness of each spring is given as k1 = 40 N/m, k2 = 50 N/m and k3 = 60 N/m.
(M-15)
14. The 200 Kg crate in Fig is suspended using the ropes AB and AC. Each rope can withstand a maximum of 10
kN before it breaks. If AB always remains horizontal, determine the smallest angle θ to which the crate can be
suspended before one of the ropes breaks.
(M-2015)
UNIT – II : EQUILIBRIUM OF RIGID BODIES
PART – A (2 MARKS)
1. Define - Equilibrium
(N-06,M-13)
A body is said to be in a state of equilibrium, if the body is either at rest or is moving at a constant velocity.
2. What is two force equilibrium principle?
(M-04)
If a body is in equilibrium acted upon by two forces they must be of collinear forces of equal magnitude and opposite
sense.
3. What is three force equilibrium principle?
(M-07)
If a body is in equilibrium acted upon by three forces, they the resultant of any two forces must be equal, opposite and
collinear with the third force.
4. What is three four equilibrium principle?
(N-13)
If a body is in equilibrium acted upon by four forces, they the resultant of any two forces must be equal, opposite and
collinear with the resultant of the other two.
5. How many equations of equilibrium are defined for a concurrent force system and coplanar force system?
(N-12)
For concurrent force system: two equations ΣH = 0, and ΣV = 0
For coplanar force system: three equations ΣH = 0, ΣV = 0 and ΣM = 0
6. State Varignon‟s theorem
(M-13, N-14)
If a number of coplanar forces are acting simultaneously on a body, the algebraic sum of the moments of all the forces
about any point is equal to the moment of the resultant force about the same point.
(ie.) F1d1 + F2d2+ F3d3+ - - -- - -- - = R × d
7. What is stable equilibrium?
(N-12)
A body is said to be in stable equilibrium, if it returns back to its original position after it is slightly displaced from its
position of rest.
8. What is unstable equilibrium?
(M-13)
A body is said to be in unstable equilibrium, if it does not returns back to its original position, and heels farther away
after slightly displaced from its position of rest.
9. What is neutral equilibrium?
(M-12)
A body is said to be in neutral equilibrium, if it occupies a new position (also remains at rest) after slightly displaced
from its position of rest.
10. What is free body diagram?
(N-08)
It is a sketch of the particle which represents it as being isolated from its surroundings. It represents all the forces
acting on it.
11. What are the characteristics of a couple?
(M-09)

The algebraic sum of the forces is zero

The algebraic sum of the moments of the forces about any point is the same and equal to the moment of the
couple itself.
12. Define moment of a force?
(M-11, M-08)
Moment of force is defined as the product of the force and the perpendicular distance of the line of action of force from
the point. It‟s unit is N-m. M=F x r in N-m
Clockwise moment → positive sign
Anticlockwise → negative sign
13. For what condition the moment of a force will be zero?
(N-11)
A force produces zero moment about an axis or reference point which intersects the line of action of the force.
14. What is the difference between a moment and a couple?
(M-15,M-08,N-12)
The couple is a pure turning effect which may be moved anywhere in its own plane, or into a parallel plane without
change of its effect on the body, but the moment of a force must include a description of the reference axis about
which the moment is taken.
15. What are the common types of supports used in two dimensions?
(N-11)
i) Roller support ii)Hinged support iii)Fixed support.
16. What are the common types of supports used in three dimensions?
(M-13)
i)Ball support ii)Ball and socket support iii)Fixed or welded support.
17. What are the common types of loads?
(N-11)
i)point load or concentrated load ii)uniformly distributed load iii)uniformly varying load
18. What is statically determinate structure?
(N-10)
A structure which can be completely analyzed by static conditions of equilibrium ΣH = 0,
ΣV = 0 and ΣM = 0 alone is called statically determinate structure.
19. What is beam?
(N-13)
A beam is a horizontal structure member which carries a load, transverse (perpendicular) to its axis and transfers the
load through support reactions to supporting columns or walls.
20. What is a point load?
(M-12)
A load acting at a point on a beam is known as a point load
21. What is a uniformly distributed load?
(M-13)
A load which is spread over a beam in such a manner that each unit length of the beam carries same intensity of the
load, is called uniformly distributed load
22. What are the difference between roller support and hinged support?
(N-09)
Roller support has the known line of action of reaction, always normal to the plane of rollers. But, hinged support has
an unknown line of action of reaction, at any angle θ with horizontal.
23. What is support reaction of beam?
(M-08)
The force of resistance exerted by the support on the beam is called as support reaction. Support reaction of beam
depends upon the type of loading and the type of support.
24. What is the difference between action and reaction?
(N-14)
Consider a ball placed on a horizontal surface. The self weight of the ball (W) is acting vertically downwards
through its centre of gravity. This force is called action. Now, the ball can move horizontally but its vertical downward
motion is resisted due to resisting force developed at support, acting vertically upwards. This force is called reaction.
25. Define the term couple
(M-06)
A couple is that two forces are of equal magnitude, opposite sensed parallel forces, which lie in the same plane.
26. What is a rigid body?
(N-07)
When a body is not subjected to collinear or concurrent force system, then the body is to be idealized as a rigid body.
27. What is the condition for Equilibrium of rigid body in two dimension?
(M-10)
For the equilibrium state of rigid body, the resultant force and the resultant moment with respect to any point is zero.
∑H = 0 ; ∑V = 0 ; ∑M = 0
28. What is Support reaction ?
(M-11)
The resistance force on the beam against the applied load at support is called support reaction.
29. What mechanics concept does the balanced teeter-totter (seesaw) signify.
(M-15)
Mechanically a seesaw is a lever and fulcrum.
30. Determine the moment of the force about point “O” for following diagram.
(N-14,M-11)
Moment = Force X moment arm
Moment arm = 4 X 2 cos 30° = 5.73 m
Moment = 40 X 5.73 = 229.23 Nm. (clockwise)
PART – B (16 MARKS)
1. Determine the resultant of the coplanar non-concurrent force system shown in fig. below. Calculate its magnitude
and direction and locate its position with respect to the sides AB and AD.
(N-12)
2. Determine the location of resultant of four forces and one couple which act on the plate as shown in figure.
(M-09)
3. Find the reactions at the supports A and B or the beam shown in figure.
(M-09)
.
4. Two beams AB and CD are shown in fig. A and D are hinged supports. B and C are roller supports.
a) Sketch the free body diagram of the beam AB & determine the reactions at the support A & B.
b) Sketch the free body diagram of the beam CD & determine the reactions at the supports C &D
(M-11)
5. Find the reactions at the supports A and B or the beam shown in figure.
(N-10)
6. A load of 3500 N is acting on the boom which is held by a cable as shown in fig, the weight of the boom can be
neglected
1. Sketch the free body diagram
2. Determine the tension in the cable BC
3. Find the magnitude and direction of the reaction at A
(M-15)
7. Four tugboats are used to bring an ocean large ship to its pier. Each tugboat exerts a 22.5 KN force in the direction
as shown in fig. Determine the equivalent force couple at O and determine a single equivalent force and its location
along the longitudinal axis of the ship.
(M-13)
8. A roller of radius r = 304.8 mm and weight = 2225N is to be pulled over a curb of height h=152.4 mm by a horizontal
force P applied to the end of the string wound around the circumference of the roller. Find the magnitude of P
required to start the roller over the curb.
(M-08)
RB COS 60 = 2225 N ; RB= 4450P= 3853.8 N
9. Reduce the system of forces shown in fig. to a force – couple system at A.
(N-11)
9. Four forces act on a 700mm X 375mm plate as shown in figure.
a) Find the resultant of these forces
b) Locate the two points where the line of action of the resultant intersects the edge of the plate.
(N-11)
UNIT – III : PROPERTIES OF SURFACES AND SOLIDS
PART – A (2 MARKS)
1. What are the types of equilibrium?
(M-11, M-13)
Stable equilibrium : The body returns back to its original position after it is slightly displaced from the position of rest.
Unstable equilibrium : The body doesn't return back to its original position after it is slightly displaced from the
position of rest.
Neutral equilibrium : The body occupies a new position (and rests) after it is slightly displaced from the position of
rest.
2. Differentiate between Centroid and Centre of gravity.
(N-11)
The centre of figures which have only area but no mass is known as centroid. Centre of gravity is a point where the
entire mass or weight of the body is assumed to be concentrated.
3. Define - Centroid axis
The axis which passes through the point, where the entire mass or weight of the
(N-09, M-12, N-13)
body is assumed to be
concentrated, is known as the centroid axis.
4. Under what conditions do the Centre of mass and Centre of gravity coincide?
(M-13)
The material must be homogeneous and (ii) the gravitational force on a body of mass 'm' must also pass through its
centre of mass.
5. Define - Moment of Inertia of an area
(N-09)
The first moment of a force about any point is the product of the force (P) and the perpendicular distance between
the point and the line of action. If this first moment is again multiplied by the perpendicular distance, the resulting
moment is the second moment of the force or moment of moment of the force. Instead of force, if the area is
considered, it is called the second moment of the area or Moment of Inertia.
6. State the second moment of area of a triangle with respect to the base.
(M-14)
IBase = bh3/12
7. Define - Parallel axis theorem
(N-12)
Parallel axis theorem : Moment of inertia of an area any axis is equal to the sum of the moment of inertia about an
axis passing through the centroid parallel, to the given axis and (b) the product of area and square of the distance
between the two parallel axes. IAB = I CG + A h2
Where, IAB = Moment of inertia of an area about any given axis (say AB)
ICG = Moment of inertia about an axis passing through the centroid
A = area of the section given
h = distance between the two parallel axes
8. State perpendicular Axis Theorem.
(M-15)
Moment of inertia of plane Iamina about an axis perpendicular to the Iamina and passing through its centroid is
equal to the sum of moment of inertia about two mutually perpendicular axes passing through the centroid and in
the plane of the lamina.
Izz = Ixx + Iyy
9. Define - Polar moment of inertia of an area and state its application.
(M-12)
Moment of inertia of an area about an axis perpendicular to the area through a pole point in the area is called polar
moment of the inertia. Polar moment of inertia has application in problems relating to the torsion of cylindrical shafts
and rotation of slabs.
10. Define - Radius of gyration.
(M-11)
The radius of gyration 'k' of any lamina about a given axis is the distance from the given axis at which all the
elemental parts of the lamina would have to be placed, so as not to alter the Moment of inertia about the given axis.
Radius of gyration, k = √I/A
11. Define - Product of inertia
(M-12)
Product of inertia of an area with respect to x and y axes is denoted by Ixy = ∫xydA where x and y are the
coordinates of an element dA of the area A.
NOTE :Ixy = 0, for a figure, which is symmetrical about either x or y axes.
12. State the salient properties of product of inertia.

(N-15)
Product of inertia Ixy is zero when x axis or y axis or both the x and y axes are axes of symmetry for the given
area.

Product of inertia may be either positive or negative.

Product of inertia of the given area with respect to its principal axes is zero.
13. Define - Principal Axis and Principal Moment of Inertia.
(M-14)
The axes about which moments of inertia is ZERO are known as principal axes.
The moment of inertia w.r. to the principal axes are called principal moments of inertia.
14. State the salient properties of product of inertia.
(N-12)
(i) Product of inertialxy is zero when x axis or y axis or both the x and y axesare axes of symmetry for the given
area.
(ii) Product of inertia may be either positive or negative.
(iii) Product of inertia of the given area with respect to its principal axes is zero.
15. State Pappus - Guldinus theorems.
(M-15, N-12, M-13)
Theorem 1 :
The area of surface of revolution obtained by revolving a line or curve is equal to the length of the generating line
or curve multiplied by the distance travelled by the centroid of the generating line / curve when it is being rotated.
Theorem 2:
The volume of a body obtained by revolving an area is equal to the generating area multiplied by the distance
traveled by the centroid of the generating area when it is being rotated.
16. Define - Moment of inertia of mass
(N-14)
Consider a body of mass m. The moment of the body with respect to the axes AA' is defined by the integral, l=∫r2dm
where, dm is the mass of an element of the body situated at a distance r from axes AA' and integration is extended
over the entire volume of the body.
17. State the relationship between the second moment of area and mass moment of Inertia for thin uniform plate.
(N-09)
Mass moment of inertia of a thin plane about an axis x - x, (Ixx) mass = p t (Ixx) area Where, (Ixx) area is the second
moment of the area of the plate about the axis xx, p is the mass density and t, thickness of the plate which is
uniform.
18. Differentiate between area moment of inertia and mass moment of inertia.
(N-13)
The Area Moment Of Inertia of a beams cross-sectional area measures the beams ability to resist bending. The
larger the Moment of Inertia the less the beam will bend. The moment of inertia is a geometrical property of a beam
and depends on a reference axis. The smallest Moment of Inertia about any axis passes through the centroid.The
Mass Moment of Inertia of a solid measures the solid's ability to resist changes in rotational speed about a specific
axis. The larger the Mass Moment of Inertia the smaller the angular acceleration about that axis for a given torque.
19. What is axis of revolution?
(M-07)
The fixed axis about which a plane curve (may be of an arc, straight line etc) or a plane area is rotated is known as
axis of revolution.
20. State the methods of determining the centre of gravity.
1. By geometrical considerations.,2. Graphical method.,3. Integration method.,4. Method of moments.
(N-08)
PART – B (16 MARKS)
1. Determine the centroid of the cross-sectional area of an unequal I-section shown below.
(N-12, M-13)
2. Locate the centroid of the plane area shown in figure.
(M-11)
3. Determine the co-ordinates of the centroid of the shaded area shown in figure.
(N-12)
4. For the plane area shown below, locate the centroid of the area.
5. Locate the centroid of area shown below.
(M- 14)
(N-11, M-09)
6. In the figure below, a solid is formed by joining a hemi sphere, a cylinder and a cone, all made out of same material.
Find the location of the centroid of this solid on the Z – axis.
(M-12, N-14)
7. Determine the moments of inertia of the area shown with respect to the centroidal axes parallel and perpendicular to
the side AB.
(M-09, N-11)
8. For the plane area shown below, determine the area moment of inertia and radius of gyration about the x – axis.
(N-14, M-13)
9. Determine the moment of inertia and radius of gyration of the T section about centroidal Y axis. Also find polar
moment of inertia.
(N-11)
10. Determine the moments of inertia Ix and Iy of the area shown below with respect to centroidal axes respectively
parallel and perpendicular to the side AB.
(M-15)
11. Compute the second moment of area of the plane surface shown below about its horizontal and vertical centroidal
axes.
(M-11)
12. Find the moment of inertia about 1–1 and 2–2 axes for the area shown in figure below.
(M-15)
13. Find the mass moment of inertia of the rectangular block shown below about the vertical y axis. A cuboid of 20 mm
x 20 mm x 20 mm has been removed from the rectangular block as shown below. The mass density of the material
of the block is 7850 kg/m3.
(N-12)
14. Determine the coordinates of the centroid of the shaded area and the moment of inertia of the cross sectional area
(I section) of the channel with respect to the y axis.
(M-15)
ii.Similar to problem 10.
UNIT – IV : DYNAMICS OF PAARTICLES
PART-A (2 MARKS)
1. What are motion curves?
(M-10)
The curves which are plotted with the position coordinate, the velocity and the acceleration against the time„t‟ are
called motion curves.
2. Differentiate between rectilinear motion and curvilinear motion.
(M-13, N-14)
Rectilinear motion: If the path traced by a point is a straight line, then the resulting motion is termed as rectilinear
motion.
Curvilinear motion: If the path traced by a point is aa curve, then the resulting motion is termed as curvilinear
motion.
3. Differentiate between uniform rectilinear motion and uniformly accelerated rectilinear motion.
(N-09)
In case of uniform rectilinear motion the velocity „ v „ will be a constant (or) the motion of a particle in which the
acceleration a of a particle is zero for every value of „ t ‟.
When the acceleration is constant in a body, which moves, in a straight line, then the resulting motion is called
uniformly accelerated rectilinear motion.
4. What is projectile motion?
(M-14, M-12)
Any object that is given some initial velocity and during the subsequent motion the object is subjected to only the
acceleration due to gravity is termed as a projectile. A projectile travels in the horizontal as well as in the vertical
directions and traces a curvilinear path. For example: The motion of a bullet fired from a gun
5. State D' Alembert's principle.
(M-15, N-13, M-09)
The force system consisting of external forces and inertia force can be considered to keep the particle in
equilibrium. Since the resultant force externally acting on the particle is not zero, the particle is said to be in dynamic
equilibrium. This principle is known as D' Alembert's principle.
6. State the work-energy principle.
(M-13)
The work done by force acting on a particle during its displacement is equal to the change in the kinetic energy of
the particle during that displacement.
Work done = Final Kinetic energy – Initial Kinetic energy = ½ ( mv22– mv12 )
7. State the law of conservation of energy.
(N-09)
"Energy can neither be created nor be destroyed. It can only be changed from one form into another form".
8. Define linear impulse or (impulse).
(M-12, N-14)
Linear impulse or impulse is the product of force acting on a body and the time elapsed.
9. What is impulsive force and impulsive motion?
(N-12)
When a large force acts on a particle for a short period of time and produces a definite change in its momentum,
then, such a force is called an impulsive force. The motion caused by such an impulsive force is known as impulsive
motion.
10. State Impulse momentum principle
(N-14)
Final momentum – Initial Momentum = Impulse of the Force.
The equation expresses that the total change in momentum of a particle during a time interval is equal to the
impulse of the force during the same interval of time.
11. State the condition for the dynamic equilibrium of a body.
(N-10, M-13)
The equation of motion can be written in the form
F – ma = 0
F + (-ma) = 0
To write the equation of dynamic equilibrium of a particle, add a friction force equal to inertial force to the external
forces acting on the particle, and equate the sum to zero.
12. State the principle of impulse and momentum or write impulse momentum equation.
(M-09)
Principle of impulse and momentum is written in the form of an equation
"Impulse = final momentum – initial momentum"
13. What is impact or collision?
(M-12)
A collision between two bodies that lasts for a very short interval of time during which period, the two bodies exert
large forces on each other is called an impact or collision.
14. Define - Line of impact.
(N-07)
A line perpendicular to the surfaces of contact during impact is known as the line of impact.
15. What is the difference between central and eccentric impact?
(M-11)
If the mass centres of the two colliding bodies lie on the line of impact, then, the impact is said to be central impact
otherwise it is eccentric.
16. Distinguish between direct impact and oblique impact.
(N-08)
If the velocities of the two colliding bodies act along the line of impact, the impact is called direct impact.If the
velocities of the two colliding bodies act along lines other than the line of impact, the impact is known as oblique
impact.
17. Distinguish between perfectly plastic impact and perfectly elastic impact.
(N-11)
In the case of perfectly plastic impact, e = 0. This means that there is no period of restitution. The two colliding
bodies join together and travel with the same velocity.
In the case of perfectly elastic impact, e = 1. This means that the relative velocity before the impact is equal to the
relative velocity after the impact.
18. Define- Linear Momentum.
(M-13)
The linear momentum of a particle is the product of mass and velocity.
19. State the Principle of conservation of linear momentum.
(M-08)
Principle of conservation of linear momentum states that if the resultant force acting on a particle is zero then the
linear momentum of the particle remains constant.ie., "Final momentum = Initial momentum"
20. Define co-efficient of restitution.
(N- 12)
The ratio of magnitudes of impulses corresponding to the period of restitution and to the period of deformation is
called coefficient of restitution.
It is also defined as the ratio of velocity of separation to the velocity of approach.
21. What is Inertia force?
(N-07)
The inertia force can be defined as the resistance to the change in the condition of rest or of uniform motion of a
body. The magnitude of the inertia force is equal to product of the mass and acceleration of the particle and it acts
in a direction opposite to the direction of acceleration of the particle. The equation of motion of the particle P.
22. What are the conditions under which the motion of a projectile is parabolic?
In the horizontal direction: x = vcosθ t t = x / vcosθ
In the vertical direction: y = vsinθ (t) - ½g(t)²
using the result above:
y = vsinθ (x / vcosθ) - ½g(x / vcosθ)²
y = xtanθ - ½g(x / vcosθ)²
(M-15)
PART – B (16 MARKS)
1. The motion of a particle is defined by the relation x = 3t4 + 4t3 – 7t2 - 5t + 8 , where x and t are expressed in
millimeters and seconds, respectively. Determine the position, the velocity and the acceleration of the particle when
t = 3s.
(N-13)
2. The motion of a particle is defined by the relation x = 3t3 – 6t2 – 12t + 5 , where x and t are expressed in meters
and seconds, respectively. Determine (a) when the velocity is zero (b) the position, the acceleration and the total
distance traveled when t = 4s.
(M-15)
3. The motion of a particle is defined by the relation x = t3– 9t2 + 24t – 8 , where x and t are expressed in meters and
seconds, respectively. Determine (a) when the velocity is zero (b) the position and the total distance traveled when
the acceleration is zero.
(M-14)
When V=0,
4. A ball is thrown vertically up with an initial velocity of 25 m/s. Calculate the maximum altitude reached by the ball
and the time t after throwing for it to return to the ground. Neglect air resistance and take the gravitational
acceleration to be constant at 9.81m/s2 .
(N-12)
5. Two trains A and B leave the same station in parallel lines. Train A starts with a uniform acceleration of 0.15m/sec2
and attains a speed of 27 kmph when the steam is reduced to keep speed constant. Train B leaves 40 seconds
later with uniform acceleration of 0.3m/sec2 to attain a maximum speed of 54 kmph. When and where will B
overtake A?
6. Two cars are traveling towards each other on a single lane road at the velocities 12 m/sec and 9 m/sec.
respectively. When 100m apart, both drivers realize the situation and apply their brakes. They succeed in stopping
simultaneously and just short of colliding. Assume constant deceleration for each case and find (a) time required for
cars to stop (b) deceleration of each car and (c) the distance traveled by each car while slowing down. Ans: t =
9.524sec, a1 = -1.26 m/sec2, a2 = -0.945 m/s2, x = 57.14m, 42.86m
(N-13)
7. Two trains A and B leave the same station on parallel lines. A starts with uniform acceleration 1/6 m/s2 and attains
a speed of 24kmph when steam is reduced to keep the speed constant. 40 seconds after B leaves with uniform
acceleration of 1/3 m/s2 to attain a maximum speed of 48 kmph. When will train B overtake train A.
(M-14)
8. Three marks A, B, C spaced at a distance of 100m are made along a straight road. A car starting from rest and
accelerating uniformly passes the mark A and takes 10 seconds to reach the mark B and further 8 seconds to reach
mark C. Calculate:(a) the magnitude of the acceleration of the car;,(b) the velocity of the car at A,(c) the velocity of
the car at B and (d) the distance of mark from starting point.
(N-10)
9. Two automobiles A and B traveling in the same direction in adjacent lanes are stopped at a traffic signal as the
signal turns green, automobile A accelerates at a constant rate of 2 m/s2. Two seconds later, automobile B starts
and accelerates at a constant rate of 3.6 m/s2. Determine (a) when and where B will over take A (b) the speed of
each automobile at that time. t = 7.85s, 61.7m, va= 15.71m/s, vb= 21.1m/s
(M-09)
10. A bus starts from rest at point A and accelerates at a rate of 0.9m/s2 until it reaches a speed of 7.2 m/s. It then
proceeds with the same speed until the brakes are applied. It comes to rest at point B, 18m beyond the point, where
the brakes are applied. Assuming uniform acceleration, determine the time required for the bus to travel from point
A to B. The distance between the points A and B is 90m.
(N-12)
11. Two electric trains A and B leave the same the same station on parallel lines. A starts with a uniform acceleration of
0.2m/s2 and attains a speed of 45 kmph, and then the speed is maintained constant. B leaves 60 seconds later with
a uniform acceleration of 0.4 m/s2 to attain a maximum speed of 72 Kmph. When will train B overtake train A.?
(M-13, N-14)
12. A body weighing 400 N is resting on a rough plane inclined at 20° to the horizontal as shown. It is pulled up the
plane from rest by means of a light flexible rope running parallel to the plane and passing over a light frictionless
pulley at the top of the plane. The portion of rope beyond the pulley hangs vertically and carries a weight of 225 N
at the end. If the co efficient of friction for the plane and the body is 0.15, find (a) tension in rope (b) acceleration of
the
body
and
(c)
distance
moved
by
the
body
in
3
seconds,
starting
from
rest.
(N-09)
400
2
0

2
2
5
13. A sphere A of weight 10N moving with a velocity of 3m/s to the right impinges with a sphere B of weight 50N moving
with a velocity of 0.6 m/s to the right. If the coefficient of restitution between the spheres is 0.75, find the loss of
kinetic energy and show that the direction of the motion of sphere A is reversed.
(M-11)
UNIT – V : FRICTION AND ELEMENTS OF RIGID BODY DYNAMICS
PART – A (2 MARKS)
1. Define – Friction
(N -13)
When two surfaces are in contact with each other and one surface tends to move with respect to other, a tangential
force will be developed at the contact surface, in the opposite direction of motion. This tangential force is called
frictional force or friction.
2. What are the types of friction?
(N -12)
Two types of friction I).Dry friction or coulomb friction II).Fluid friction
Two types of dry friction i).static friction ii).dynamic friction
Dynamic friction is further classified into I).sliding friction II).rolling friction
3. Define - Coefficient of friction
(M-13)
The ratio of limiting friction to the normal reaction is known as coefficient of friction. It is denoted by the symbol µ
,Coefficient of friction = limiting friction / normal reaction
4. Define - Angle of repose
(M-11)
The angle of the inclined plane at which the body tends to slide down is known as angle of repose
5. What is simple contact friction?
(M-11)
The friction force is the resisting force developed at the contact surface of two bodies due to their roughness and when
the surface of one body moves over the surface of an another body.
6. What are the applications of simple contact friction?
Ladder friction,
(N-09)
Wedge friction, Screw friction, Belt friction
7. What is rolling resistance?
(M-12)
When one body is made to roll freely over an another body, a resistance is developed in the opposite direction known
as rolling resistance.
8. What is impending motion?
(M-08)
The state of motion of a body which is just about to move or slide is called impending motion.
9. What is angle of repose?
(M-15)
Angle of repose is equal to angle of friction.
10. State the laws of dynamic friction
i). the frictional force always acts in the opposite direction to that the body moves
ii).coefficient of kinetic friction is less than the coefficient of static friction
iii).in moderate speeds, the force of friction remains constant and it decreases with the increase of speed
iv).the magnitude of dynamic friction bears a constant ratio to the normal reaction between the two surfaces.
(N-12)
11. State the laws of static friction
(N-10)
i). the frictional force always acts in the opposite direction to that the body moves
ii).the frictional force does not depend on the shape and area of contact of the bodies
iii).the frictional force depends on the degree of roughness of the contact area between two bodies.
iv).the frictional force is equal to the force applied to the body, so long as the body is at rest
v). limiting friction force bears a constant ratio to the normal reaction between the surfaces of contact
12. What is coefficient of rolling resistance?
(N-09)
Horizontal distance of point of resistance measured from centre of wheel known as coefficient of rolling resistance
13. Define - Angle of friction
( M-12)
It is the angle between the line of action of the total reaction of one body on another and the normal to the common
tangent between the bodies when motion is impending
14. What is coefficient of static friction?
(N-11)
The ratio of limiting friction to the normal reaction is known as coefficient of static friction. It is denoted by the symbol µ
,Coefficient of static friction = limiting friction (F) / normal reaction (N)
15. What is the condition in terms of efficiency for a machine to be self locking?
(N-08)
If the friction angle φ is larger than the lead angle θ, the screw is said to be self locking .i.e., load will remain in place
even after the removal of effort.
16. What are the laws of sliding friction?
(M-11)
The frictional force always acts in the opposite direction to that the body moves the magnitude of the sliding friction
bears a constant ratio to the normal reaction between the surfaces of contact in moderate speeds, the force of friction
remains constant and it decreases with the increase of speed
17. State the coloumb‟s laws of dry friction.
(M-13)
The frictional force always acts in the opposite direction to that the body moves the limiting friction force bears a
constant ratio to the normal reaction between the surfaces of contact the frictional force is independent of the area of
contact between the two surfaces, and it depends on the of roughness of the surface. The magnitude of friction force
is equal to the force, which tends to move the body
18. What is Limiting friction?
(N-12)
The maximum resistance offered by a body against the external force which tends to move the body is called limiting
force of friction.
19. What is Coefficient of friction ?
µ=Fm/ NR
Fm - Force of friction.
NR - Normal reaction.
(N-10)
20. What is Angle of friction ?
(N-08)
Angle between normal reaction and reaction is called angle of friction. tan φ=Fm/NR =µ
21. What is Simple contact friction ? Write applications of simple contact friction
(M-09)
The type of friction between the surface of block and plane is called simple contact friction.
Applications are Ladder friction , Screw friction & Belt friction
22. Write expression for Belt friction
(M-13)
T2/ T1 = e µ θ
T1→ Tension in slack side
T2→ Tension in tight side
µ → Coefficient of friction between belt and wheel θ → Angle of contact
23. What is Rolling resistance & Coefficient of resistance?
(M-14)
When a body is made to roll over another body the resistance developed in the opposite direction of motion is called
the rolling resistance. R cosα is called rolling resistance.
Horizontal distance b is called as coefficient of resistance.
b=Pr/ W
P→ applied force , r→ radius of the body , W→ weight of the body
24. What are the various types of motion of rigid bodies?
1.Translation
a) Rectilinear→ straight-line path motion b) Curvilinear→ curved path motion
2.Rotation (with respect to a fixed point)
3.Rotation& Translation (General plane method)
(M-11)
PART – B (16 MARKS)
1. A body lying on a horizontal plane is moved slowly along the plane when a force of 100 N is applied to the body.
Also, a force of 90 N is applied to the body at an angle of 30° to the horizontal, moves the body slowly along the
same plane. Determine the weight of the body and coefficient of friction.
(M-15)
2. Two blocks A of weight 48N and B of weight 80 N are on rough horizontal surface and are connected by an
inextensible string. Find the minimum value of „P‟ applied at B at an angle of 30° to the plane, just to move the
system. If the co efficient of friction between the block A and the ground is 0.3 and that between the block B and
the ground is 0.25, find the tension in the string.
(M-12)
3. An effort of 200 N is required just to move a certain body up an inclined plane of angle 15°, the force acting
parallel to the plane. If the angle of inclination is made 20° the effort required, again parallel to the plane, is
found to be 230 N. Find the weight of the body and coefficient of friction.
(N-09)
4. Two blocks A & B of weights 1kN and 2kN respectively are in equilibrium as in fig-1. If the co efficient of friction
between the two blocks and also the block and the floor is 0.3, find the force „P‟ required to move the block B.
(M-13)
5. What is the least value of „P‟ required to cause the motion of the system shown in fig-3, impend? Assume the co
efficient of friction on all contact surfaces as 0.2.
(M-11)
6. What should be the value of θ in fig-4, which will make the motion of 900N block down the plane to impend?
The co efficient of friction for all the contact surfaces is 1/3. 29.05°
(M-08)
7. In the engine system shown in fig the crank AB has a constant angular velocity of 3000 rpm. For the crank
position indicated, find the

angular velocity of the connecting rod

velocity of the piston.
(N-14)
8. The linear velocity of the slider shown in fig is 2m/s to the left along the horizontal plane. Determine the velocity
of the crank AB at the instant shown using instantaneous centre method.
(M-13)
9. Determine the distance S to which the 90kg painter can climb without causing the 4-m ladder to slip at its lower
end A. The top of the 15kg ladder has a small roller and at the ground the coefficient of static friction is 0.25.
The mass center of the painter is directly above her feet.
(M-15)