Code: D-02                                                                               Subject: APPLIED MECHANICS

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1 A must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1 A    Choose the correct or best alternative in the following:                                         (2x10)

a. If the line of action of all the forces meet at a single point, then the force system is known as  

(A)  Collinear                                      (B)  Coplanar

(C)   Concurrent                                  (D)  Parallel.

b. A Free body diagram of an hinged support contains

(A) Vertical reaction only

(B) Horizontal reaction only

       (C)  Both horizontal and vertical reactions

(D)  Horizontal, vertical reactions and a moment

c. For a cantilever beam of length ‘L’ having a point load ‘P’ at its free end, the bending moment at the fixed end is given by

(A) PL                                               (B)  (P/2) L

                                                                       (C)  P/L           (D)  2 PL

             d.  The kinetic energy of a body of mass ‘m’ moving with a velocity ‘v’ is equal to

(A) mv                                               (B) (m²v)/2

      (C) (mv)/2                                           (D) (mv²)/2

             e.   A triangular three member frame is an example of ________________ frame

(A) Perfect                                         (B) Imperfect

                                                                       (C) Redundant (D) Collapsible

             f.    The unit of bending moment in SI units is

(A)  Kg/m                                            (B) Kg-m

                                                                       (C) N/m           (D) N-m

     B State which of the statement is true and which are false.

g.   First moment of area about the centroidal axis is positive

             h.   A body moving along a curved path has only tangential acceleration

             i.  The instantaneous center of rotation of a body lies always outside the body

             j.    Velocity of a body is a scalar quantity

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   Define Lami’s theorem.                                                                                      (2)

             b.   A smooth sphere weighing 200 N is lying in a triangular groove as shown in Fig.1. Draw the free body diagram and find the reactions at the surfaces of contact, assuming groove is also smooth.   (8)

c.   A system of forces in equilibrium is shown in Fig.2. Determine the force               

      ‘P’ and the angle ‘q’.                                                                                                    (6)

                                                                                  Fig.2

Q.3     a.   Derive the expression for moment of inertia of a circular lamina of radius ‘r’ about a horizontal axis passing through the centre.                               (8)

         b.   Find the distance of centroid of the shaded portion shown in Fig.3 about

               axis AB.                                                                                                            (8)

Q.4     a.   Define:                                                

(i) Static friction

(ii) Coefficient of friction

(iii) Angle of friction

(iv) Angle of repose                                                                                (8)

b.   A body resting on a horizontal rough surface requires a pull of 180 N inclined at 30^o to the surface for just to move it. It was found that a push of 220 N inclined at 30^o to the surface was able to just move the body. Determine the weight of the body and coefficient of friction between the body and the surface.                                                                   (8)

Q.5           Using method of joints, determine the forces and their nature in all the members of the pin jointed plane truss shown in Fig. 4. Tabulate the results.                                                                (16)

Q.6     a. Explain (i) Impulse-momentum principle (ii) Law of conservation of    

linear momentum.                                                                                           (8)

            b.        The angle of rotation of a body is given by the equation:

q = 2 t³ – 5 t² + 8 t + 6

Where q is in radians and t is in secs.

               Determine (i) angular velocity (ii) angular acceleration of the body

                        When t = 0 and t = 4 secs.                                                                            (8)

Q.7   a.         Define:

(i) Hooke’s law

(ii) Moment of Inertia

(iii) Poisson’s ratio

(iv) Thermal stress                                                                        (8)

b.      A hollow cast iron cylinder 4 m long, 300 mm outer diameter, and

                      thickness of metal 50 mm is subjected to a central load on the top when 

                      standing straight. The stress produced is 75000 k N/m². Assume   

                      Young’s modulus for cast iron as 1.5x10⁸ kN/m². Determine the  

                      magnitude of the load applied, longitudinal strain and total decrease in 

                      length.                                                                                                             (8)

Q.8     a.      Derive the Torque equation for pure torsion of shaft stating clearly the  

assumptions made.                                                                                              

(6)

             b.   Determine the diameter of a solid shaft which will transmit 90 kW at      160 rpm, if the shear stress in the shaft is limited to 60 N / mm². Find also the length of the shaft, if the twist must not exceed 1 degree over the entire length. Take C = 8 x 10⁴ N/mm² (10)

Q.9     a.   Define point of contraflexure.                                                                              (2)

b.   For the beam loaded as shown in Fig.5, draw the shear force and bending moment diagrams.                                                                    (14)

                                                         Fig. 5