1 (a) Draw typical cross section of a road and explain the
parts. (06 Marks)

(b) Distinguish between detention dams and diversion dams.
(04 marks)

(c) Explain the classification of bridges on the basis of
bridge floor and position of high flood level. (05 Marks)

(d) Write a note on geotechnical engineering. (05 Marks)

2(a) State and explain with neat sketches (i) principle of
transmissibility of forces, (ii) principle of physical independence of forces
and (iii) principle of superposition of forces. (09 Marks)

(b) Explain the resolution and composition of forces in
Cartesian coordinate system. (06 Marks)

(c) A door needs 7500 N-mm to open it. Mr.X applies the
force at the edge of the door shutter which is at a distance of 750 mm from the
hinge and Mr.Y applies it at a distance of 500 mm from the hinge. What forces
have they to apply to open the door? (05 Marks)

3(a) State and prove Lami’s theorem. (06 Marks)

(b) State and prove Varignon’s theorem of moments. (08
Marks)

(c) Define the terms resultant force, composition of force
and resolution of force. (06 Marks)

4 (a) Differentiate between hinged support and roller
support. (04 Marks)

(b) Explain different types of beams with neat sketches. (06
Marks)

(c) Write notes on dry friction and fluid friction. (04
Marks)

(d) A body resting in a plane (horizontal0 required a pull
of 18 KN inclined at 30

^{0}to plane just to move it. It was also found that a push of 22 KN inclined at 30^{0}to the plane just moved the body. Determine the weight of the body and the coefficient of friction. (06 Marks)
5 (a) Derive an expression for centroid of a triangle of
base ‘b’ and depth ‘d’. (06 Marks)

(b) Obtain centroidal distance for a sector of angle 2α from
first principles. Use it to locate centroid of semicircular and quarter
circular plane laminae. (08 Marks)

(c) Determine the centroid of a quarter-circular area of
radius ‘r’ from first principles. (06 Marks)

6 (a) State and prove perpendicular axis theorem. (06 Marks)

(b) Derive an expression for moment of inertia of a
semicircular lamina and quarter circle of radius “R”. (08 Marks)

(c) Radius of a circle is 2 cm. Determine the moment of
inertia about its diametrical axis. What should be the radius of the semi
circle to get the same moment of inertia? (06 Marks)

7(a) Write a note on curvilinear motion. (06 Marks)

(b) A stone is thrown vertically upward from the top of the
tower 30m high with a velocity of 16 m/s. find (i) the highest elevation for
the stone.(ii) the time required for the stone to cross the top of tower during
its downward motion and corresponding velocity. (08 Marks)

(c) The motion of a particle is defined by the relation x =
4t

^{3}-9t^{2}+12t-8. Determine the position and acceleration when velocity = 0 m/s. (06 Marks)
8(a) Define the terms angle of projection, horizontal range,
vertical height and time of flight in projectile motion. (08 Marks)

(b) A particle is projected at such an angle with the
horizontal that the horizontal range is three times the greatest height
attained. Calculate the angle of projection. (04 Marks)

(c) Two trains A and B of same length 100m move in the same
direction. It is found that 20 seconds are required to cross one another if
train a moves with 50% of velocity of train B. calculate the velocity of both
the trains. (04 Marks)

(d) Calculate the safe driving speed of a curve with a
radius of 300m, the super elevation being 0.056. Assume maximum value of µ =
0.15 (04 Marks)

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