Section A
Q1.
(a) The Porter governor has equal arms each 300 mm long and pivoted on the axis of rotation. Each ball has a mass of 5 kg and the mass of the sleeve is 20 kg. The radius of rotation of the ball is 150 mm when the governor begins to lift and 200 mm when the governor is at maximum speed. Find the range of speed of the governor.
(b) A U tube open to atmosphere at both ends contains a column length l of a certain liquid. Find the natural frequency of oscillation of the liquid column.
(c) A member formed by connecting a steel bar to an aluminium bar is shown in the figure below. Calculate the magnitude of the force P that will cause the total length of the bar to decrease by 0.5 mm. The Young's modulus for steel and aluminium are 2 × 105 MPa and 7 × 104 MPa respectively. The cross-sectional area of the steel bar is 25 cm2 and of the aluminium bar is 100 cm2.
(d) Enlist the different Bravais crystal systems. Also write the relationship between their primitives and between their angles.
(e) Determine the Miller indices of a set of parallel planes, which create intercepts in the ratio of 2a : 3b and parallel to the z-axis. Consider the lattice to be cubic with a = b = c = 4 Å. Calculate the interplanar spacing of the planes.