Mechanical Engineering Gate 2015 Set-1 Questions with Answer

Ques 53 GATE 2015 SET-1

A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ________.

Ques 54 GATE 2015 SET-1

Consider a slider crank mechanism with nonzero masses and inertia. A constant torque τ is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, θ, versus time

Ques 55 GATE 2015 SET-1

A pinion with radius r₁, and inertia I₁ is driving a gear with radius r₂ and inertia I₂. Torque τ₁ is applied on pinion. The following are free body diagrams of pinion and gear showing important forces (F₁ and F₂) of interaction. Which of the following relations hold true?

Ques 56 GATE 2015 SET-1

Temperature of nitrogen in a vessel of volume 2 m³ is 288 K. A U-tube manometer connected to the vessel shows a reading of 70 cm of mercury (level higher in the end open to atmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325 bar, acceleration due to gravity is 9.81 m/s² and density of mercury is 13600 kg/m³. The mass of nitrogen (in kg) in the vessel is ________

Ques 57 GATE 2015 SET-1

A well insulated rigid container of volume 1 m³ contains 1.0 kg of an ideal gas [C_p = 1000 J/(kg·K) and C_v = 800 J/(kg·K)] at a pressure of 10⁵ Pa. A stirrer is rotated at constant rpm in the container for 1000 rotations and the applied torque is 100 N·m. The final temperature of the gas (in K) is ________

Ques 58 GATE 2015 SET-1

Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, 20 percent of the mass is extracted for process heating and the remaining steam expands isentropically to 9 kPa. Inlet to turbine: P = 14 MPa, T = 560°C, h = 3486 kJ/kg, s = 6.6 kJ/(kg·K) Intermediate stage: h = 2776 kJ/kg Exit of turbine: P = 9 kPa, h_f = 174 kJ/kg, h_g = 2574 kJ/kg, s_f = 0.6 kJ/(kg·K), s_g = 8.1 kJ/(kg·K) If the flow rate of steam entering the turbine is 100 kg/s, then the work output (in MW) is ________

Ques 59 GATE 2015 SET-1

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,

Ques 60 GATE 2015 SET-1

A Carnot engine (CE-1) works between two temperature reservoirs A and B, where T_A = 900 K and T_B = 500 K. A second Carnot engine (CE-2) works between temperature reservoirs B and C, where T_C = 300 K. In each cycle of CE-1 and CE-2, all the heat rejected by CE-1 to reservoir B is used by CE-2. For one cycle of operation, if the net Q absorbed by CE-1 from reservoir A is 150 MJ, the net heat rejected to reservoir C by CE-2 (in MJ) is ________.

Ques 61 GATE 2015 SET-1

Air enters a diesel engine with a density of 1.0 kg/m³. The compression ratio is 21. At steady state, the air intake is 30x10^-3 kg/s and the net work output is 15 kW. The mean effective pressure (in kPa) is ________.

Ques 62 GATE 2015 SET-1

A stream of moist air (mass flow rate = 10.1 kg/s) with humidity ratio of 0.01 kg/kg dry air mixes with a second stream of superheated water vapour flowing at 0.1 kg/s. Assuming proper and uniform mixing with no condensation, the humidity ratio of the final stream (in kg/kg dry air) is ________.

Ques 63 GATE 2015 SET-1

Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is

Ques 64 GATE 2015 SET-1

A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to center of gravity (CG) of the mobile and the rest of the dimensions of the mobile phone are shown. The mobile is kept on a flat horizontal surface.

Ques 65 GATE 2015 SET-1

A precision instrument package (m=1 kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural frequency significantly lesser than 60 Hz, so that the effect of damping may be ignored. The stiffness (in N/m) of the required mounting pad is ________.