GATE 2009 Mechanical Engineering Question Paper

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1 GATE 009 Mechanical Engineering Question Paper. For a matrix [M]= x [M]. The value of x is given by GATE MECHANICAL ENGINEERING 009 (ME) GATE 009 Mechanical Engineering Question Paper Q. No. 0 Carry One Mark Each 4, the transpose of the matrix is equal to the inverse of the matrix [M] T = 4 4. The divergence of the vector field xzî xyĵ yz kˆ at a point (,, ) is equal to The inverse Laplace transform of is (s s) + e t e t e t + e t 4. If three coins are tossed simultaneously, the probability of getting at least one head /8 /8 / 7/8. If a closed system is undergoing an irreversible process, the entropy of the system Must increase Always remains constant Must decrease Can increase, decrease or remain constant 6. A coolant fluid at 0 C flows over a heated flat plate maintained at a constant temperature of 00 C. The boundary layer temperature distribution at a given location on the plate may be approximated as T = exp (y) where y (in m) is the distance normal to the plate and T is in C. If thermal conductivity of the fluid is.0w/mk, the local convective heat transfer coefficient (in W/mK) at that location will be A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.0 m. It expands quasistatically at constant temperature to a final volume of 0.00 m. The work output (in kj) during this process will be In an ideal vapour compression refrigeration cycle, the specific enthalpy of refrigerant (in kj/kg) at the following states is given as: Inlet of condenser: 8 Exit of condenser: 6 Exit of evaporator: The COP of this cycle is Page of

2 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) 9. A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressor is designated as state and state respectively. Potential and kinetic energy changes are to be ignored. The following notations are used: v= specific volume and P=pressure of the gas. The specific work required to be supplied to the compressor for this gas compression process is Pdv vdp v (P P ) P (v v ) 0. A block weighing 98N is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is = 0.A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 00N. What will be the tension, T (in N) in the cable if the man is just able to move the block to the right? = 0. G T 00N. If the principal stresses in a plane stress problem, are = 00MPa, = 40MPa, the magnitude of the maximum shear stress (in MPa) will be A simple quick return mechanism is shown in the figure. The forward to return ratio of the quick return mechanism is :. If the radius of the crank O P is mm, then the distance 'd' (in mm) between the crank centre to lever pivot centre point should be Q O P d O Page of

3 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME). The rotor shaft of a large electric motor supported between short bearings at both deflection of.8mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is A solid circular shaft of diameter d is subjected to a combined bending moment M and torque, T. The 6 material property to be used for designing the shaft using the relation M T d is ultimate tensile strength (S u ) tensile yield strength (S y ) torsional yield strength (S sy ) endurance strength (S e ). The effective number of lattice points in the unit cell of simple cubic, body centered cubic, and face centered cubic space lattices, respectively, are,,,,4,,4,4,4 6. Friction at the tool-chip interface can be reduced by decreasing the rake angle increasing the depth of cut decreasing the cutting speed increasing the cutting speed 7. Two streams of liquid metal, which are not hot enough to fuse properly, result into a casting defect known as cold shut swell sand wash scab 8. The expected time (t e ) of a PERT activity in terms of optimistic time (t 0 ), pessimistic time (t p ) and most likely time (t l ) is given by to 4tl tp to 4tp tl te te 6 6 to 4tl tp to 4tl tl te te 9. Which of the following is the correct data structure for solid models? solid part faces edges vertices solid part edges faces vertices vertices edges _ faces solid parts vertices faces edges solid parts 0. Which of the following forecasting methods takes a fraction of forecast error into account for the next period forecast? simple average method moving average method weighted moving average method exponential smoothening method Q. No. 6 Carry Two Marks Each. An analytic function of a complex variable z = x + iy is expressed as f(z) = u (x, y) + iv (x, y) where I =. If u = xy, the expression for v should be (x y) k x y + k y x + k (x y) + k Page of

4 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) dy. The solution of x + y = x 4 6 with the condition y() = is dx y = x 4 x 4 4x 4 x 4 y y = y = x x +. A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration Y of (x +y) on path AB traversed in a counterclockwise sense is B + A X 4. The distance between the origin and the point nearest to it on the surface z = + xy is. The area enclosed between the curves y = 4x and x = 4y is The standard deviation of a uniformly distributed random variable between 0 and is 7 7. Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from 0cm to 0cm. The pressure in the 0cm pipe just upstream of the reducer is 0kPa. The fluid has a vapour pressure of 0kPa and a specific weight of kn/m. Neglecting frictional effects, the maximum discharge (in m /s) that can pass through the reducer without causing cavitation is In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid, flowing at kg/s with C p = 4kJ/kgK, enters the heat exchanger at 0 C while the cold fluid has an inlet temperature of C. The overall heat transfer coefficient for the heat exchanger is estimated to be kw/m K and the corresponding heat transfer surface area is m. Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: = exp ( NTU). The exit temperature (in C) for the cold fluid is Page 4 of

5 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) 9. In an air-standard Otto cycle, the compression ratio is 0. The condition at the beginning of the compression process is 00kPa and 7 C. Heat added at constant volume is 00kJ/kg, while 700kJ/kg of heat is rejected during the other constant volume process in the cycle. Specific gas constant for air=0.87 kj/kgk. The mean effective pressure (in kpa) of the cycle is An irreversible heat engine extracts heat from a high temperature source at a rate of 00kW and rejects heat to a sink at a rate of 0kW. The entire work output of the heat engine is used to drive a reversible heat pump operating between a set of independent isothermal heat reservoirs at 7 C and 7 C. The rate (in kw) at which the heat pump delivers heat to its high temperature sink is You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices, expressed in terms of the two-dimensional velocity fields in the xyplane, are made available. P. u = y, v = x Q. u = xy, v = 0 R. u = x, v = y Which flow(s) should be recommended when the application requires the flow to be incompressible and irrotational? P and R Q Q and R R. Water at C is flowing through a.0km long G.I pipe of 00mm diameter at the rate of 0.07m /s. If value of Darcy friction factor for this pipe is 0.0 and density of water is 000kg/m, the pumping power (in kw) required to maintain the flow is Consider steady-state heat conduction across the thickness in a plane composite wall (as shown in the figure) exposed to convection conditions on both sides. h i, T,i h 0, T,0 L L Given: H i = 0W / m K; h 0 = 0W / m K; T,i = 0C; T,0 = C; k = 0W / mk; k = 0W / mk; L = 0.0m and L = 0.m. Assuming negligible contact resistance between the wall surfaces, the interface temperature, T (in C), of the two walls will be Page of

6 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) 4. The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, R dp is given by the expression u(r) = 4 dx r dp where is a constant. The average velocity R dx of fluid in the pipe is r X U(r) R dp R dp R dp 8 dx 4 dx dx dp dx R. A solid shaft of diameter, d and length L is fixed at both the ends. A torque, T 0 is applied at a distance, L/4 from the left end as shown in the figure given below. T 0 L/4 L/4 The maximum shear stress in the shaft is 6T d 0 T d 0 8T d 0 4T d 0 6. An epicyclic gear train is shown schematically in the adjacent figure The sun gear on the input shaft is a 0 teeth external gear. The planet gear is a 40 teeth external gear. The ring gear is a 00 teeth internal gear. The ring gear is fixed and the gear is rotating at 0 rpm ccw 4 (ccw=counterclockwise and cw=clockwise) The arm 4 attached to the output shaft will rotate at 0 rpm ccw 0 rpm cw rpm cw rpm ccw Page 6 of

7 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) 7. A forged steel link with uniform diameter of 0mm at the centre is subjected to an axial force that varies from 40kN in compression to 60kN in tension. The tensile (S u ), yield (S y ) and corrected endurance (S e ) strengths of the steel material are 600MPa, 40MPa and 40MPa respectively. The factor of safety against fatigue endurance as per Soderberg s criterion is An automotive engine weighing 40kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 6MN/m while the stiffness of each rear spring is MN/m. The engine speed (in rpm), at which resonance is likely to occur, is A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is.6kn/m and the damping constant of the damper is 400Ns/m. If the mass is 0kg, then the damping factor (d) and damped natural frequency (f n ), respectively, are 0.47 and.9hz 0.47 and 7.48Hz and.hz and 8.0Hz 40. A frame of two arms of equal length L is shown in the adjacent figure. The flexural rigidity of each arm of the frame is EI. The vertical deflection at the point of application of load P is PL EI PL EI L P PL EL 4PL EI L 4. A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of L/ from the hinge so that the rod swings to the L/ right. The reaction at the hinge is L -P 0 P P/ P/ Page 7 of

8 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) 4. Match the approaches given below to perform stated kinematics / dynamics analysis of machine. Analysis Approach P. Continuous relative rotation. D Alembert s principle Q. Velocity and acceleration. Grubler s criterion R. Mobility. Grashoff s law S. Dynamic-static analysis 4. Kennedy s theorem P-,Q-,R-,S-4 P-,Q-,R-4,S- P-,Q-4,R-,S- P-4,Q-,R-,S- 4. A company uses units of an item annually. Delivery lead time is 8 days. The recorder point (in number of units) to achieve optimum inventory is Consider the following Linear Programming Problem (LPP): Maximize z = x + x Subject to x 4 x 4 x + x 8 x 0, x 0 The LPP has a unique optimal solution The LPP is infeasible The LPP is unbounded The LPP has multiple optimal solutions 4. Six jobs arrived in a sequence as given below: Jobs Processing Time (days) I 4 II 9 III IV 0 V 6 VI 8 Average flow time (in days) for the above jobs using Shortest Processing Time rule is Minimum shear strain in orthogonal turning with a cutting tool of zero rake angle is Electrochemical machining is performed to remove material from an iron surface of 0mm 0mm under the following conditions: Inter electrode gap = 0.mm Supply voltage DC = V Specific resistance of electrolyte = cm Atomic weight of Iron =.8 Valency of Iron = Faraday 's constant = 9640 Coulombs The material removal rate (in g/s) is Page 8 of

9 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) 48. Match the following NC Code Definition P. M0. Absolute coordinate system Q. G0. Dwell R. G04. Spindle stop S. G90 4. Linear interpolation P-,Q-,R-4,S- P-,Q-4,R-,S- P-,Q-4,R-,S- P-4,Q-,R-,S- 49. What are the upper and lower limits of the shaft represented by 60 f 8? Use the following data: Diameter 60 lies in the diameter step of 0-80mm Fundamental tolerance unit, i, in m=0.4d / D, where D is the representative size in mm; Tolerance value for IT8=i. Fundamental deviation for f shaft = -.D 0.4 Lower limit = 9.94mm, Upper Limit = 9.970mm Lower limit = 9.94mm, Upper Limit = mm Lower limit = 9.970mm, Upper Limit = 60.06mm Lower limit = mm, Upper Limit = mm 0. Match the items in Column I and Column II. Column I Column II P. Metallic Chills. Support for the core Q. Metallic Chaplets. Reservoir of the molten metal R. Riser. Control cooling of critical sections S. Exothermic Padding 4. Progressive solidification P-,Q-,R-,S-4 P-,Q-4,R-,S- P-,Q-4,R-,S- P-4,Q-,R-,S- Common Data Questions: & The inlet and the outlet conditions of stream for an adiabatic steam turbine are as indicated in the notations are as usually followed h = 00kJ/kg V = 60m/s Z = 0m P = MPa (Figure) H = 600kJ/kg V = 00m/s Z = 6m P = 70kPa. If mass flow rate of steam through the turbine is 0kg/s, the power output of the turbine (in MW) is Assume the above turbine to be part of a simple Rankine cycle. The density of water at the inlet to the pump is 000kg/m. Ignoring kinetic and potential energy effects, the specific work (in kj/kg) supplied to the pump is Page 9 of

10 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) Common Data Questions: & 4 Radiative heat transfer is intended between the inner surfaces of two very large isothermal parallel metal plates. While the upper plate (designated as plate ) is a black surface and is the warmer one being maintained at 77ºC, the lower plate (plate ) is a diffuse and gray surface with an emissivity of 0.7 and is kept at 7ºC. Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as W/m K 4. The irradiation (in kw/m ) for the upper plate (plate ) is If plate is also a diffuse and gray surface with an emissivity value of 0.8, the net radiation heat exchange (in kw/m ) between plate and plate is Common Data Questions: & 6 Consider the following PERT network: The optimistic time, most likely time and pessimistic time of all the activities are given in the table below Activity Optimistic time (days) Most likely time(days) Pessimistic time (days) The critical path duration of the network (in days) is The standard deviation of the critical path is Page 0 of

11 GATE 009 Mechanical Engineering Question Paper GATE MECHANICAL ENGINEERING 009 (ME) Linked Answer Questions: Q.7 to Q.60 Carry Two Marks Each Statement for Linked Answer Questions: 7 & 8 In a machining experiment, tool life was found to vary with the cutting speed in the following manner: Cutting speed (m/min) Tool life (minutes) The exponent (n) and constant (k) of the Taylor s tool life equation are n = 0. and k= 40 n = and k= 4860 n = and k = 0.74 n = 0. and k =. 8. What is the percentage increase in tool life when the cutting speed is halved? 0% 00% 00% 400% Statement for Linked Answer Questions: 9 & 60 A 0º full depth involute spur pinion of 4mm module and teeth is to transmit kw at 960rpm. Its face width is mm. 9. The tangential force transmitted (in N) is Given that the tooth geometry factor is 0. and the combined effect of dynamic load and allied factors intensifying the stress is.; the minimum allowable stress (in MPa) for the gear material is Page of

GATE Question Paper & Answer Keys

GATE Question Paper & Answer Keys Question Paper & Answer Keys Index 1. Question Paper Analysis. Question Paper & Answer keys : 080-617 66, info@thegateacademy.com Copyright reserved. Web:www.thegateacademy.com ANALYSIS OF GATE 009 Mechanical