17929
21718
3 Hours / 100 Marks Seat No.
Instructions – (1) All Questions are Compulsory.
(2) Answer each next main Question on a new page.
(3) Illustrate your answers with neat sketches wherever
necessary.
(4) Figures to the right indicate full marks.
(5) Assume suitable data, if necessary.
(6) Use of Non-programmable Electronic Pocket
Calculator is permissible.
(7) Mobile Phone, Pager and any other Electronic
Communication devices are not permissible in
Examination Hall.
Marks
1. Attempt any TEN of the following: 20
a) Define efficiency of machine.
b) State the condition for irreversibility of machine.
c) Write the expression for the velocity ratio of double purchase
crab.
d) Define ideal machine?
e) Differentiate between mass and the weight.
f) Resolve a given force acting away from the point to a force
and the couple acting at the point.
g) Give an example for an anticlockwise couple stating its
magnitude and units.
P.T.O.
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Marks
h) State the graphical conditions of equilibrium for a non-concurrent
coplanar force system.
i) Define coefficient of static friction for any pair of surfaces.
j) If two forces are acting at a point, state the conditions of
equilibrium.
k) Define the centroid for a circle with reference to axis of
symmetry.
l) Two forces 9 kN each from the sides of a right angled triangle,
find their Resultant.
m) A triangle has a base 30 cm and height 40 cm, locate its
centroid from the apex.
n) A force of 20 N is acting southwest; Find its rectangular
components.
2. Attempt any TWO of the following: 16
a) A drum weighing 60 N and holding 400 N of water is to be
raised from a well by means of differential axle having
diameters 100 mm and 60 mm, with the effort wheel of 500 mm
diameter. If a force of 120 N is required to lift. Find M.A.,
U.R. and efficiency for the machine.
b) A regular pentagon has five forces acting along the radii with the
first force 25 N being horizontal, All the forces are acting away
from the center. The remaining forces are 15 N, 20 N, 5 N and
10 N in the anticlockwise direction. Find their resultant.
c) Find the resultant of the force system Q. 2(b), graphically.
3. Attempt any TWO of the following: 16
a) A single purchase crab has teeth on the spur as 100 and on
the pinion 20. The diameter of the load axle is 80 mm and the
effort wheel is 160 mm. If 20 N is required to lift a load
300 N, what effort is required to lift a load 300 N, what
effort is required lift a load of 500 N. Also find the law of
machine.
b) A continuous string carries two weights 60 N and W. The string
subtends and angle of 60° and 45° with the horizontal due to the
weights. Find the unknown weight W and tension in the string.
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Marks
c) Find the unknown weight W and tension in the string
graphically for the set up Q. 3 (b).
4. Attempt any TWO of the following: 16
a) A force system has four parallel vertical forces acting at 1m,
2m, 3m and 4m from point ‘O’. The first two forces are
10 N and 40 N, acting upwards the remaining two forces are
15 N and 25 N acting downwards. Find the magnitude and
position of the resultant from ‘O’.
b) A simply supported beam has 4m span with left hand support
as Roller and right hand support as hinge. Two point loads
10 kN and 20 kN acting at 1 m and 3 m from roller. The
20 kN is inclined at 60° with horizontal. Both forces are
acting downwards. Find the reactions graphically.
c) A square has sides 2 m carrying forces 10 N, 5 N, 15 N and
20 N in anticlockwise directions along sides AB, BC, CD and
DA. Find the magnitude, direction and location of the
Resultant from point A.
5. Attempt any TWO of the following: 16
a) (i) A force of 2000 N acts an angle of 55°. Find its
components along 110° and 320° with X-axis.
(ii) A three forces 3 N, 9 N and 14 N are acting along the
sides of triangle AB, BC and AC respectively. Calculate
the moments of all the forces about point C, if
AB = BC = AC = 0.75 m.
b) A body weighting 200 N rests on an inclined plane making an
angle of 30° with the horizontal. If the coefficient of friction
between the body and the plane is 0.2, what force is required
(i) parallel to the plane
(ii) horizontally acting to move the body upwards.
c) A ladder weighting 600 N rests against a smooth wall on a
rough floor having coefficient of friction 0.3. If the length
of the ladder is 4.5 m, will the ladder stands in equilibrium
when it makes an 60° with the floor.
P.T.O.
17929 [4]
Marks
6. Attempt any TWO of the following: 16
a) (i) Define centroid and center of gravity with the help of
sketches and state their importance in engineering
applications.
(ii) Find the centroid of Lamina shown in Fig. No. 1.
Fig. No. 1
b) Find the centroid of the Fig. No. 2, w.r.t. both the reference
axes x-x, y-y.
Fig. No. 2
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Marks
c) (i) Find the C.G. of the frustum of the conce having top
diameter 20 cm, bottom diameter 40 cm and height 30 cm.
(ii) Find the centroid of a T section having flange
(20 m × 60 mm) and web (20 mm × 60 mm) shown in
Fig. No. 3.
Fig. No. 3
