### ENGG MECHANICS Question Bank UNIT

```ENGG MECHANICS
Question Bank
UNIT-1
1.Three forces of magnitude 150 N, 300 N and 500 N are acting at the origin O(0,0,0) and are directed from the
points A(3,2,4), B(3,-2,-4) and C(-1,-3,-4) respectively to the origin. Determine the magnitude of the resultant.(
Aug/Sep 2008)
2. Determine the magnitude and direction of a single force which keeps the system in equilibrium. The system
of forces acting is shown in Figure ( Aug/Sep 2008)
15kN
7 kN
3m
8 kN
6m
10 kN
3. (a) The resultant of the two forces when they act at an angle of 650 is 20 N. If the same forces are acting at
right angles their resultant is 16.5 N. Determine the magnitude of the two forces.
(b) A force of 100N makes angles of 300, 600 and 1000 with x,y, z axes respectively.
Find the components of the force along the x,y and z axes. (Aug/Sep 2008)
4. Determine the magnitudes of F1 and F2 for the following system of forces
which are in equilibrium as shown in figure
5. Find the magnitude of two forces such that if they act at right angles, their resultant is √10 N, but if they act
at 60o, their resultant is √13 N. (Aug/Sep 2008)
6. Two forces are acting at a point O as shown in figure. Determine the resultant in magnitude and direction of
the force. (June-2010)
Q=100 KN
300
P=50 KN
O
150
7. Three forces of magnitude 40 kN, 15 kN and 20 kN are acting at a point O as shown in figure. The angles
made by 40 kN, 15 kN and 20 kN forces with X- axis are 60o, 120o and 2400 respectively. Determine the
magnitude and direction of the resultant force. (June-2010)
15 KN
40 KN
300
600
600
20 KN
UNIT II
1. An effort of 200 N is required just to move a certain body up an inclined plane of angle 150 the acting
parallel to the plane. If the angle of inclination of the plane made 200 the effort required is found to be 230 N.
Find the weight of the body and coefficient of friction. (May 2009)
2. Determine the resultant of the system of forces shown in fig (Aug/Sep 2008)
3. Determine the push Necessary to move a body up the plane at 200 to the horizontal, if the weight if the body
is 200 N and inclination of push is 100 to the horizontal.
4. A ball of weight Q = 12 N rests in a right - angled trough, as shown in figure. Determine the forces exerted
on the sides of the trough at D and E if all surfaces are perfectly smooth. (June-2010)
5.Two blocks A and B ,connected by a horizontal rod are lying in a two rough planes as shown in fig. the
coefficient of friction are 1.3 between Block A & surface and 0.4 between Block B & surface. If the block B
weighs 100N what is the smallest weight of Block A , That will keep in the system in equilibrium.
A
B
600
6. A body of 20 KN rests on a horizontal plane. Just to move the body along horizontal direction, the minimum
force required is 7.28 KN. Determine the least inclined force required to just draw the body along the same
horizontal line.
7.A ladder of length 10 m an weight 20 KN is placed against a smooth vertical wall with its lower end 8m from
the wall. In this position, the ladder is just to slip. Determine (1) the coefficient of friction between floor and
UNIT III
1.Find the centroid of the area shown in figure ( Aug/Sep 2008)
2. Determine the coordinates of the centroid of the quadrant PQ of the arc of a
circle if raduis ‘r’ show in figure ( Aug/Sep 2008)
3.Find the centroid of the plane area shown in figure ( Aug/Sep 2008)
4. Determine the centre of gravity of a homogeneous hemisphere of radius ‘a’. (Aug/Sep 2008)
5. Find the centroid of the area shown figure. (Aug/Sep 2008)
6. Find the centroid of the shaded area shown in figure. (Aug/Sep 2008)
7. a) What is centroid and center of
gravity? State the differences clearly.
b) Determine the centroid of the parabolic spandrel as shown in figure. (June 2010)
8. Find the centroid of the shaded lamina shown in the fig.
9. Find the centroid of shaded area shown in fig.
10.A thin homogeneous wire is bent into a triangular shape ABC such that AB = 240 mm, BC = 260 mm
and AC = 100 mm. Locate the C.G. of the wire with respect to coordinate axes. Angle A is right angle.
11.A solid body is formed by joining the base of a right circular cone of height H to the equal base of a
right circular cylinder of height h. Calculate the distance of the centre of mass of the solid from its plane
surface, when H=120mmand h = 30mm.
12. Find centre of gravity of a 100 mm X 150 mm X 30 mm T section
UNIT IV
1. Derive an equation for moment of inertia of rectangular section about centroidal axis.
2. Derive an equation for moment of inertia of hollow rectangular section about centroidal axis
3. Derive an equation for moment of inertia of circular section about centroidal axis
4. Derive an equation for moment of inertia of hollow circular section about centroidal axis
5. State and prove the theorem of perpendicular axis, as applied to moment of inertia.
6. Prove the parallel axis theorem
7. Find the moment of inertia of the plane area shown in figure 4 about X and Y axes through its centroid.
(Aug/Sep
2008)
8. State and prove parallel axis theorem of area moment of inertia. (June 2010)
9. Determine the product of inertia of a rectangle of base ‘a’ and height ‘h’ about x axis and y axis by
direct integration. (June 2010)
UNIT V
1. Calculate the forces included in the members of the pin-jointed truss shown in
figure. Show the values on a neat diagram of the truss. (Aug/Sep 2008)
2. Calculate the forces induced in the member of a pin-jointed truss shown in figure. (Aug/Sep 2008)
3.A pin jointed frame is supported at A and B and loaded as shown in figure 5. Find
the forces in all the members of the frame and state in each case, whether the force
is tensile or compressive. (Aug/Sep 2008)
4. Tabulate the member forces for the structure shown in figure.(Aug/Sep 2008)
5. What are the assumptions made
6. Find the forces in all the
(June 2010)
for forces in members of a perfect frame? (June 2010)
members of the truss as shown in the figure using method of joints.
UNIT VI
1. The motion of the particle is defined by the relation x = 6t4 + 8t3 - 14t2-10t + 16, where x and t are
expressed in meters and records, respectively. Determine the position, the velocity, and the acceleration as the
particle when t= 3s. (Aug/Sep 2008)
2. A car is tested for acceleration and braking. In the street - start acceleration test, the elapsed time is 8 seconds
for a velocity increase from 8 km/h to 80 km/h. In the braking test, the distance traveled is 40m during braking
to a stop from 80 km / hr. Assuming constant values of Acceleration and deceleration,
Determine
i. the acceleration during the street - start test
ii. The deceleration during the braking test. (Aug/Sep 2008)
3. (a) Define curvilinear linear motion of a particle.
(b) Show that the system of the effective forces for a rigid slab in plane motion reduces to a single vector,
and express the distance from the mass center G of the slab to the line of action of this vector in terms of the
centroidal radius of gyration k of the slab, the magnitude a of the acceleration of G, and the angular
acceleration α. (Aug/Sep 2008)
4. Bars AB and BE, each of weight 3.2 kg are welded together and are pin-jointed to two links AC and BD. The
assembly is released from rest in the position shown in figure 6 and Neglecting the masses of the links
determine
(a) the acceleration of the assembly
(b) the forces in the links. (Aug/Sep 2008)
6.a) Derive the equations of motion of a particle with uniform acceleration.
b) Two bodies of weight 20 N and 10 N are connected to the two ends of a light inextensible string, passing
over a smooth pulley. The weight of 20 N is placed on a horizontal surface while the weight of 10 N is hanging
free in air. The horizontal surface is a rough one, having coefficient of friction between the weight 20 N and the
plane surface equal to 0.3, determine:
i) The acceleration of the system.
ii) The tension in the string. (June-2010)
UNIT VII
1. A 500kg communications satellite is in a circular geosynchronous orbit and complete one revolution about
the earth in 23 hrs and 58min at an attitude of 35800 km above the surface of the earth. The radius of the earth
is 6510km. Determine the Kinetic energy of the satellite. (Aug/Sep 2008)
2. Express the acceleration of gravity ‘g’ at an altitude ‘h’ above the surface of the earth in terms of the
acceleration of gravity
go. at the surface the earth,the altitude h, and the radius R of the earth. (Aug/Sep
2008)
3. (a) State the Principle
of conservation of momentum
(b) A golfer hits a 46gm ball with an initial velocity of 48 m/s at angle of 240 with the horizontal. Determine
i. the initial KE of the ball
ii. the KE of the ball when it reaches its maximum height. (Aug/Sep 2008)
4. A solid cylinder of weight W and radius ‘r’ rolls, down an inclined plane which
makes angle θ with the horizontal axis. Determine the minimum coefficient of
friction and the acceleration of the mass center for rolling, without slipping(Aug/Sep 2008)
5.A body of mass 18 kg slides up an incline of 300 under the action of an applied
force 300N along the incline and in the presence of friction, µ = 0.2. If the body moves from rest determine,
after a period of 6 secs;
i. Acceleration of the body
ii. Distance traveled by the body
iii. Kinetic energy of the body
iv. Work done on the body. (Aug/Sep 2008)
6. A 2kg collar can slide without friction along a horizontal rod as shown infigure and is released from rest at
A. The undeformed lengths of springs BA & CA are 30cm and 25cm respectively and the constant of each
spring is 490KN/m. Determine the velocity of the collar when it has moved 3 cm to the right. (Aug/Sep 2008)
20
kg
10 kg
Direction of Motion
Direction of Motion
7. In the pulley system shown in figure the masses of blocks A and B are 20 kg and 10 kg respectively. The
masses of pulley and rope may be neglected. Find the velocity of the blocks 5 sec after they start from rest.
(June-2010)
UNIT VIII
1. Determine the reactions at supports as shown in figure using the principle of virtual work(June-2010)
2. A uniform ladder of weight 250 N as shown in the figure rests with its upper end against a smooth
0
vertical wall and its foot on a rough horizontal ground making an angle of 45 with the ground. Find the
force of friction of the ground using the method of virtual work. (June-2010)
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