Mechanical Eng Optional Paper 2012 (Maharashtra)

Q1.

(a) 1. A beam ABC is loaded and supported as shown in the fig. Find the magnitude of the clockwise moment M to be applied at C so that the reaction at B will be 30 kN upward and then draw the shear force and bending moment diagrams for the beam. ,40 kN ,10 kN 20 \text kN/m _{\rm A} anna mann Е B thin 2m 2m 1 m 2m 2 m (Fig. not to scale)

(b) Explain the working of universal dividing head.

(c) Explain construction and working of hydroelectric power plant. State advantages of Hydroelectric power plant. Describe the construction and working principle of Babcock and Wilcox water 10^\circ

(d) tube boiler with a neat sketch. Also list the different mountings and accessories on it. P.T.O.

Q2.

(a) 2. Answer the following sub-questions : A vibrating system consists of a mass of 50 kg, spring of stiffness 30 kN/m and a damper. The damping provided is only 20% of the critical value. Determine the damping factor
(i) the critical damping coefficient
(ii) (iii) the natural frequency of damped vibrations. the logarithmic decrement
(iv) (v) the ratio of two consecutive amplitudes.

(b) A semi-elliptic leaf spring used for Automobile suspension consists of three extra full-length leaves and graduated length leaves, including the master leaf. The centre to centre distance between two eyes of the spring is 1 m. The maximum force that can act on the spring is 75 kN. For each leaf, the ratio of width to thickness is 9 :
1. The modulus of elasticity of the leaf material is 207000 N/mm2. The leaves are pre-stressed in such a way that when the force is maximum, the stresses induced in all leaves are same and equal to 450 \text N/mm^2. Determine : $
(i) the width and thickness of the leaves. the initial nip; and (ii) $ the initial preload required to close the gap C between extra full-length
(iii) leaves and graduated-length leaves. How a 3 D Geometric model may be represented and what is parametric modelling

(c) and when is it used?