Section A
Q1.
(a) A cord ACB 5 m long is attached at points A and B to two vertical walls 3 m apart as shown in the figure. A pulley C of negligible radius carries a suspended load of 200 N and is free to roll without friction along the cord. Determine the position of equilibrium as defined by the distance X, that the pulley will assume and also the tensile force in the cord.
(b) For a beam of hollow rectangular section of outer geometry of b × d and the inner geometry of b1 × d1, compute the area moment of inertia about its axis passing through its C.G. Also compute the area moment of inertia about a line passing through the base and also compute the same about a line passing through the vertical side. Compare the results and offer your remarks if the ratio of b : d = 1 : 2 units and in the same scaling the ratio of b1 : d1 = 0.8 : 1.6 units.
(c)
(i) Explain about a double slider crank chain and its inversions.
(ii) The distance between two parallel shafts is 18 mm and they are connected by an Oldham's coupling. The driving shaft revolves at 160 rpm. What will be the maximum speed of sliding of the tongue of the intermediate piece along the groove?
(d) A rotor has a mass of 10 kg and is mounted midway on a 20 mm diameter horizontal shaft supported at the ends by two bearings. The bearings are 1 m apart. The shaft rotates at 2000 rpm. If the centre of the mass of the rotor is 0.11 mm away from the geometric centre of the rotor due to a certain manufacturing defect, find the amplitude of the steady-state vibration. Take E = 200 GN/m^2. Assume the shaft to be simply supported.
