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

duration of the activities marked in days
D,1O
8\H,1O

C,4
M,8
The project can be completed
(a) ranging from 18, 19 days
(c) ranging from 24, 26 days
Data for Q.73 — 74 are provided beneath. Solve the issues and select accurate
The state of stress at a point ‘P’ in a 2 dimensional loading is such that the Mohr’s circle is a
point located at 175 MPa on the positive normal stress axis.
73. Determine the maximum and minimum principal stresses respectively from the Mohr’s
circle
(a) + 175 MPa, -175 MPa
(b) + 175 MPa, -175 MPa
(c) 0, -175 MPa
(d) 0, 0
71. The linear acceleration of the reel is
/ ( (hub radius)
2
(r2 +k2)
(b) gk2 (c) grk
(r +k2) (r2+k2)
(d) mgr2 (r2 +k2)
74. Determine the directions maximum and minimum principal stresses at the point ‘P’ from
the Mohr’s circle
(a) 0, 900
(b) 9o,o
(c) 450, 135°
(d) all directions
Data for Q.75 — 76 are provided beneath. Solve the issues and select accurate answers.
The circular disc shown in its plan view in the figure rotates in a plane parallel to the
horizontal plane about the point 0 at a uniform angular velocity o. 2 other points A and B
are located on the line OZ at distances rA and r8from 0 respectively.
75. The velocity of point B with respect to point A is a vector of magnitude
(a) 0
(b) o)(r8 —rA)and direction opposite to the direction of motion of point B
(c) o)(r8 —rA)and direction identical as the direction of motion of point B
(d) o(r8 —rA)and direction being from 0 to Z
76. The acceleration of point B with respect to point A is a vector of magnitude
(a) 0
(b) o)(r8 —rA)and direction identical as the direction of motion of point B
(c) o(r8 —rA)and direction opposite to the direction of motion of point B
(d) o(r8 —rA)and direction being from Z toO
Data for Q.77 — 78 are provided beneath. Solve the issues and select accurate answers.
A uniform rigid slenderbar of mass 10 kg, hinged at the left end is suspended with the
help of spring and damper arrangement as shown in the figure where K = 2kN/m, C
=500 Ns/m and the stiffness of the torsional spring K0 is one kN/m/rad. Ignore the hinge
dimensions.
77. The un-damped natural frequency of oscillations of the bar about the hinge point
is
(a) 42.43 rad/s
(b) 30 rad/s
(c) 17.32 rad/s
(d) 14.14 rad/s
Data for Q.78 — 80 are provided beneath. Solve the issues and select accurate answers.
78. The damping coefficient in the vibration formula is provided by
(a) 500 Nms/rad
(b) 500 N/(m/s)
(c) 80 Nms/rad
(d) 80 N/(m/s)
79. Z2 and Z4 are
(a) 64 and 45
(b) 45 and 64
(c) 48 and 60
(d) 60 and 48
80. The center distance in the 2nd stage is
(a) 90 mm
(b) 120 mm
(c) 160 mm
(d) 240 mm
Data for Q.81 — 82 are provided beneath. Solve the issues and select accurate answers.
A syringe with a frictionless plunger contains water and has at its end a 100 mm long needle
of one mm diameter. The internal diameter of the syringe is 10 mm. Water density is 1000
kg/m3. The plunger is pushed in at 10 mm/s and the water comes out as a jet.
81. Assuming ideal flow, the force F in Newton’s needed on the plunger to push out the water
is
(a) 0
(b) 0.04
(c) 0.13
(d) 1.15

82. Neglect losses in the cylinder and presume fully developed laminar viscous flow throughout
the needle; the Darcy friction factor is 64/Re. Where Re is the Reynolds number. provided that
the viscosity of water is 1.0 x i0 kg/sm, the force F in newtons needed on the plunger is
(a) 0.13
(b) 0.16
(c) 0.3
(d) 4.4
Data for Q.85 — 86 are provided beneath. Solve the issues and select accurate answers.
Nitrogen gas (molecular weight 28) is enclosed in a cylinder by a piston, at the initial condition
of two bar, 298 K and one m3. In a particular process, the gas slowly expands under isothermal
condition, until the quantity becomes 2m3. Heat exchange occurs with the atmosphere at 298
K during this process.
85. The work interaction for the Nitrogen gas is
(a) 200 kJ
(b) 138.6 kJ
(c) two kJ
86. The entropy change for the Universe during the process in kJ/K is
(a) 0.4652
(b) 0.0067
(c) 0
(d) -0.6711
Data for Q.87 — 88 are provided beneath. Solve the issues and select accurate answers.
A refrigerator based on ideal vapour compression cycle operates ranging from the temperature
limits of —20°C and 40°C. The refrigerant enters the condenser as saturated vapour and
leaves as saturated liquid. The enthalpy and entropy values for saturated liquid and vapour at
these temperatures are provided in the table beneath.
87. The value of the temperatur
e
gradient in the glass at the water-glass interface
is
(a) -2 x i04 (b) 0.0 (c) 0.5 x
i04
(d) two x i04
88. The heat
transfer
coefficient h in WJm2 K
is
(a) 0.0 (b) 4.8 (c) six (d) 750
87. If refrigerant circulation rate is 0.025 kg/s, the refrigeration effect is equal to
(a) 2.1 kW
(b) 2.5 kW
(c) 3.0 kW
(d) 4.0 kW
88. The COP of the refrigerator is
(a) 2.0
(b) 2.33
(c) 5.0
(d) 6.0
Data for Q.89 — 90 are provided beneath. Solve the issues and select accurate answers.
A cylinder is turned on a lathe with orthogonal machining principle. Spindle rotates at
200 rpm. The axial feed rate is 0.25 mm per revolution. Depth of cut is 0.4mm. the rake
angle is 10°. In the analysis it is obtained that the shear angle is 27.75°.
89. The thickness of the produced chip is
(a) 0.511 mm
(b) 0.528 mm
(c) 0.818 mm
(d) 0.846 mm
90. In the above problem, the coefficient of friction at the chip tool interface found using
Earnest and Merchant theory is
(a) 0.18
(b) 0.36
(c) 0.71
(d) 0.908
T(°C) hf(kJ/kg) hg(kJ/kg) sf(kJ/kg K) sg(kJ/kg K)
-20 20 180 0.07 0.7366
40 80 200 0.3 0.67

Earning:   Approval pending.