Indian Institute of Technology Madras (IIT-M) 2003 M.Tech Mechanical Engineering mechanical engg-gate - Question Paper

is made of steel for which the value of E is 2.lxlO11Pa. What is the critical speed of rotation of
the shaft?
(a) 60 Hz
(b) 90 Hz
(c) 135 Hz
(d) 180 Hz
43. Square key of side ‘d/4’ every and length I is used to transmit torque ‘T’ from the shaft of
diameter ‘d’ to the hub of a pulley. Assuming the length of the key to be equal to the
thickness of the pulley, the avg. shear stress developed in the key is provided by
(a) 4T
(b) 16T
(c) 5T
(d) 16T
44. In a band brake the ratio of tight side band tension to the tension on the slack side is 3. If
the angle of overlap of band on the drum is 180° the coefficient of friction needed ranging from
drum and the band is
(a) 0.20
(b) 0.25
(c) 0.30
(d) 0.35
45. A water container is kept on a weighting balance. Water from a tap is falling vertically into
the container with a quantity flow rate of Q; the velocity of the water when it hits the water
surface is U. At a particular instant of time the total
mass of the container and water is m. the force registered by the weighing
balance at this instant of time is
(a) mg + pQU
(b) mg + 2p QU
(c) mg + pQU2/2
(d) pQU2/2
46. In a counter flow heat exchanger, for the hot fluid the heat capacity = 2k]/kg K, mass flow
rate = five kg/s, inlet temperature = 150°C, outlet temperature = 100°C. for the cold fluid, heat
capacity = four kJ/kg K, mass flow rate = 10 kg/s, inlet temperature=20°C. Neglecting heat
transfer to the surroundings, the outlet temperature of the cold fluid in °C is
(a) 7.5
(b) 32.5
(c) 45.5
(d)70.0
47. Air flows through a venturi and into atmosphere. Air density is p; atmospheric pressure is
Pa; throat diameter is D exit diameter is D and exit velocity is U. the throat is connected to a
cylinder containing a frictionless piston attached to a spring. The spring constant is k. the
bottom surface of the piston is exposed to atmosphere. Due to the flow, the piston moves by
distance x. assuming incompressible friction less flow, x is
(a) (pQU2/2)D
(b) (pU2/8k) [2y - 1
(c) (pU2/2k) [2T — one irD
(d) (pU2/8k) [4— one ,rD

Earning:   Approval pending.