1(a) What are the methods for
finding out the resultant force for a given system of forces? (4 Marks)

(b) Discuss the classification of
couples and explain clearly the difference between a positive couple and a
negative couple. (5 Marks)

(c) Show 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. (6 Marks)

(d) A tricycle weighing 200 N has
a small wheel symmetrically placed 500 mm in front of two large wheels which
are placed 400 mm apart. If the centre of gravity of the cycle be at a
horizontal distance of 150 mm from the rear wheels and that of the rider, whose
weight is 150 N, be 100 mm from the rear wheels, find the thrust on the ground
under the different wheels. (5 Marks)

2(a) Explain Routh’s rule for
finding out the moment of inertia of an area. Explain where it is used and why?
(4 marks)

(b) Obtain a relation for the
maximum and minimum horizontal force required to maintain equilibrium of a body
lying on a rough inclined plane. (6 Marks)

(c) What is a ladder? How will
you find out the frictional force between the ladder and floor? (4 Marks)

(d) a right circular cylinder of
12 cm diameter is joined with a hemisphere of the same diameter face to face.
Find the greatest height of the cylinder, so that c.g. of the composite section
coincides with the plane of joining the two sections. The density of the
material of hemisphere is twice that of the material of the cylinder. (6 Marks)

3(a) Obtain an equation for the
maximum mechanical advantage and maximum efficiency of a machine. (6 Marks)

(b) What is a screw jack? On what
principle does it work? Derive a relation for the velocity ratio of a simple
screw jack and differential screw jack. (6 Marks)

(c) State the difference between
Weston’s differential pulley block and a geared pulley block. (4 Marks)

(d) A stone is thrown vertically
upwards, from the ground, with a velocity 49 m/s. After 2 seconds, another
stone is thrown vertically upwards from the same place. If both the stones
strike the ground at the same time, find the velocity, with which the second
stone was thrown upwards. (4 Marks)

4 (a) At what angle, the projectile
should be projected in order to have maximum range? Justify your answer by
calculations. (6 Marks)

(b) Explain the term ‘recoil of
gun’. Explain the method of determination of the velocity of the bullet. (6
Marks)

(c) A train of mass 200 tonnes is
ascending a track, which has an inclination of 1 in 100, the resistance being
75 N per tonne. What is the acceleration of the train when its speed has
reached 18 km per hour, if the power developed by the engine is 450 kW. (4
Marks)

(d) A wheel rotates for 5 seconds
with a constant angular acceleration and describes during this time 100
radians. It then rotates with a constant angular velocity and during the next
five seconds describes 80 radians. Find the initial angular velocity and the
angular acceleration. (4 Marks)

5(a) What are statically
indeterminate problem? Explain the procedure for solving such problems. (6
Marks)

(b) Explain the procedure for
finding out the stresses developed in a body due to change of temperature. (6
marks)

(c) Define strain energy and
explain how it is stored in a body? (4 Marks)

(d) A round bar 40 mm diameter is
subjected to an axial pull of 80 kN and reduction in diameter was found to be
0.007 mm. Find Poisson’s ratio and Young’s modulus for the material of the bar.
Take value of shear modulus as 40 GPa. (4 Marks)

6(a) Explain briefly the
relationship between shear force and bending moment at a section. (4 Marks)

(b) Explain by mathematical
expression, that the shear stress abruptly changes at the junction of the
flange and web of an I-section and a T-section. (6 Marks)

(c) Show that for a rectangular
section, the distribution of shearing stress is parabolic. (6 Marks)

(d) A rectangular beam 60 mm wide
and 150 mm deep is simply supported over a span of 4 meters. If the beam is subjected
to a uniformly distributed load of 4.5 kN/m, find the maximum bending stress
induced in the beam. (4 Marks)

7(a) What is moment area method?
Explain the two Mohr’s theorems, as applicable to the slope and deflection of a
beam. (6 Marks)

(b) Derive an expression for the
angle of twist in the case of a member of circular cross-section subjected to
torsional moment. (6 Marks)

(c) Describe briefly the various
ways, in which a riveted lap joint or butt joint can fail. (4 Marks)

(d) A cantilever beam 120 mm wide
and 200 mm deep is 2.5 m long. Find the uniformly distributed load, the beam
should carry to produce a deflection of 5 mm at its free end. Take E = 200 GPa.
(4 Marks)

8(a) Show that in the case of a
thin cylindrical shell subjected to an internal fluid pressure, the tendency to
burst lengthwise is twice as great as in a transverse section. (6 Marks)

(b) State the difference between
a perfect frame and an imperfect frame. (4 Marks)

(c) Describe the procedure for
drawing the vector diagram of a truss subjected to horizontal loads. (6 Marks)

(d) a steam boiler 800 mm
diameter is made up of 10 mm thick plates. If the boiler is subjected to an
internal pressure of 2.5 MPa, find the circumferential and longitudinal
stresses induced in the boiler plates. (4 Marks)