## Elements of Civil Engg. & Engg. Mechanics - Dec 2014

### First Year Engineering (P Cycle) (Semester 1)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1(a)** Briefly explain the scope of any four fields
of civil engineering. (10 marks)
**1(b)** Resolve 400 N force acting on a block as shown in
fig 1(b)

i)into horizontal and vertical components

ii)Along the inclined plane and right angles to the plane.

(10 marks)
**10(a)** What is a Centrifugal Force? What is Super elevation?(4 marks)
**10(b)** Determine the position at which the ball is thrown up the plane will strike the
inclined plane as shown in Figure 10(b). The initial velocity is 30 m/s and angle of projection
is tan^{-1}(4/3) with horizontal.
(8 marks)
**10(c) ** A stone is dropped from the top of the tower 50 m high. A t the same time another stone is thrown up from the foot of the tower with a velocity of 25 m/s. At what distance from the top and after how much time the two stones cross each other(8 marks)
**2(a)** Write shorts on :

i) Shoulders

ii)Kerbs

iii)Traffic separators

iv)Subgrade (10 marks)
**2(b)** Explain different type of force systems? (10 marks)
**3(a)** Two forces of 800 N and 600 N act at a point as s
hown in fig 3(a). Theresultant of the two forces is 1200 N. Determine the angle between the forces and the direction of the resultant.

(10 marks)
**3(b)** Determine the resultant of the forces acting on a body as shown in fig 3(b).

(10 marks)
**4(a)** 26kN force is the resultant of the two forces, on
e of which is as shown in fig4(a). Determine the other force.

(10 marks)
**4(b)** State and prove Varignon's theorem of moments. (10 marks)
**5(a)** State and prove Lami's theorem(8 marks)
**5(b)** Determine the support reactions for the overhanging beam shown in fig 5(b).

(12 marks)
**6(a)** Determine the reactions at contact points for the spheres A,B and C as shown in Fig 6(a). It is given that WA = WB, WC = 6k N, dA = dB = 500 mm, dC = 800 mm

(10 marks)
**6(b)** What is the Value of 'P' in the system shown in fig 6(b)
to cause the motion to impend to the left? Assume the pulley is smooth and co-efficient of friction between the other contact surfaces is 0.20.

(10 marks)
**7(a)** Determine the centroid of a semi-circular lamina of Radius "R" by the method of integration. (8 marks)
**7(b)** Calculate the polar moment of inertia of the shaded area as shown in Fig 7(b).

(12 marks)
**8(a)** Determine the centroid of the section of the concrete dam as shown in fig 8(a).

(8 marks)
**8(b)** Determine the moment of inertia of a triangle of base width 'b' and height 'h' about its base. Also determine the moment of inertia about the centroidal axis parallel to the base. (12 marks)
**9(a)** What is a Projectile? Define the following terms briefly
:(i) Angle of projection, (ii) Horizontal Range, (iii) Vertical Height and (iv)Time of flight(10 marks)
**9(b)** A Burglar's car starts an acceleration of 2 m/s^{2}. A police vigilant party came after 5 s and continued to chase the Burglar's car with a uniform velocity of 20 m/s. Find the time taken in which the police van will overtake the car. (10 marks)