Consider sand casting of a cube of edge length a. A cylindrical riser is placed at the top of the casting. Assume solidification time, t, oc V/A, where V is the volume and A is the total surface area dissipating heat. If the top of the riser is insulated, which of the following radius/radii of riser is/are acceptable? a (A) 3 (B) (C) 1/4 (D) Which of these processes involve(s) melting in metallic workpieces? (A) Electrochemical machining (C) Laser beam machining (B) Electric discharge machining (D) Electron beam machining The velocity field in a fluid is given to be =(4xy)i+2(x-y)j. Which of the following statement(s) is/are correct? (A) The velocity field is one-dimensional. (B) The flow is incompressible. (C) The flow is irrotational. (D) The acceleration experienced by a fluid particle is zero at (x = 0, y = 0). For a dynamical system governed by the equation, x(t)+2wx(t)+wx(t) = 0, R the damping ratio is equal to log, 2. The displacement x of this system is measured during a hammer 2 test. A displacement peak in the positive displacement direction is measured to be 4 mm. Neglecting higher powers (>1) of the damping ratio, the displacement at the next peak in the positive direction will be mm (in integer).