Mechanical Engineering Gate 2017 Set-1 Questions with Answer

Ques 53 GATE 2017 SET-1

A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm², length = 1 m, Young's modulus = 100 GPa) from a height H of 10 mm as shown. If g = 10 m/s², the maximum compression of the elastic bar is ________ mm.

Ques 54 GATE 2017 SET-1

A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the undeformed rectangle are given by P(0,0), Q(4,0), R(4,3), S(0,3). The rectangle is subjected to uniform strains, ε_xx = 0.001, ε_yy = 0.002, γ_xy = 0.003. The deformed length of the elongated diagonal, upto three decimal places, is ________ units.

Ques 55 GATE 2017 SET-1

A horizontal bar, fixed at one end (x=0), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by E(x) = 100e^-x GPa, where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is ________ mm.

Ques 56 GATE 2017 SET-1

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100 rpm. Let the number of teeth on the sun, planet and outer gears to be 50, 25, and 100, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is ________.

Ques 57 GATE 2017 SET-1

For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is ________ radian/s.

Ques 58 GATE 2017 SET-1

The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100 K, the change in molar specific enthalpy is ________ J/mol.

Ques 59 GATE 2017 SET-1

A heat pump absorbs 10 kW of heat from outside environment at 250 K while absorbing 15 kW of work. It delivers the heat to a room that must be kept warm at 300 K. The Coefficient of Performance (COP) of the heat pump is ________.

Ques 60 GATE 2017 SET-1

One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at constant volume, c_v = 1000 J/kg.K) at 1 bar, and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100 kJ of work is done on the system by a stirrer. The increase in entropy of the system is ________ J/K.

Ques 61 GATE 2017 SET-1

The pressure ratio across a gas turbine (for air, specific heat at constant pressure, c_p = 1040 J/kg.K and ratio of specific heats, γ = 1.4) is 10. If the inlet temperature to the turbine is 1200 K and the isentropic efficiency is 0.9, the gas temperature at turbine exit is ________ K.

Ques 62 GATE 2017 SET-1

Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 100 kPa, the temperature is 30°C and the relative humidity is 55%. Given that the saturation pressure of water at 30°C is 4246 Pa, the mass of water vapor per kg of dry air is ________ grams.

Ques 63 GATE 2017 SET-1

Air contains 79% N₂ and 21% O₂ on a molar basis. Methane (CH₄) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of N₂ in the products is ________.

Ques 64 GATE 2017 SET-1

The damping ratio for a viscously damped spring mass system, governed by the relationship m(d²x/dt²) + c(dx/dt) + kx = F(t), is given by

Ques 65 GATE 2017 SET-1

A thin uniform rigid bar of length L and mass M is hinged at point O, located at a distance of L/3 from one of its ends. The bar is further supported using springs, each of stiffness k, located at the two ends. A particle of mass m = M/4 is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about O, the natural frequency of the system is