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GATE 2019 Revision Test-4

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Question 1

A shaft, which is coupled with a flywheel, undergoes a static deflection of 20 mm. The critical speed of the shaft in rad/sec is:

Question 2

A riveting machine is driven by a motor of 5 kW. The actual time to complete one riveting operation is 1.5s and it absorbs 10 kN-m of energy. The moving parts including the flywheel are equivalent to 200 kg at 0.5 radius. Speed of flywheel (in rad/s) after riveting, if it was 350 rpm before riveting will be

Question 3

An inventor company challenged that his machine has the following specifications:
Temperature limits ... 755 °C and 23 °C
Power developed ... 72 kW
Fuel burned per hour ... 3.8 kg
Heating value of the fuel ... 75650 kJ/kg
State whether his claim is possible or not

Question 4

A heat engine have an efficiency of 70% is used to drive a refrigerator having a coefficient of 5. The energy observed from low temperature reservoir by the refrigerator for each kJ of energy absorbed from high temperature source by the engine is:

Question 5

In an internal combustion engine, during the compression stroke the heat rejected to the cooling water is 60kJ/kg and the work input is 110kJ/kg. Calculate the change in internal energy of the working fluid stating whether it is a gain or loss.

Question 6

A machine supported symmetrically on four springs has a mass of 80 kg. The mass of the reciprocating parts is 2.2 kg which move through a vertical stroke of 100 mm with simple harmonic motion. The machine rotates at 800 rpm. Assuming no damping, the combined stiffness of the springs, so that the force transmitted to the foundation is 1/20th of the impressed force will be _________ (N/mm).

Question 7

Find the increase in unavailable energy associated with transfer of 800kJ of heat from a constant temperature system at 600K to another constant temperature at 400K. The ambient temperature is 300K.

Question 8

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100rpm. 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 _________.

Question 9

An ideal brayton cycle without regeneration has pressure ratio of 6. Air inlet to compressor is 0.1MPa and 30^OC. The maximum temperature that can be attained in a cycle is 900^oC.The compressor and turbine efficiencies are 0.9 and 0.95 respectively. Heat supplied per kW of output obtained____________?

Question 10

The ratio of the natural frequencies of system A to B is_____________.
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Question 11

Refrigerant vapor enters into the compressor of a standard vapor compression cycle at - 10 °C (h= 402 kJ/kg) and leaves the compressor at 50 °C (h= 432 kJ/kg). It leaves the condenser at 30 °C (h= 237 kJ/kg). The COP of the cycle is ________

Question 12

The number of degree of freedom for the mechanism shown will be.

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Question 13

A refrigerator uses R-134a as its refrigerant and operates on an ideal vapour-compression refrigeration cycle between 0.14 MPa and 0.8 MPa. If the mass flow rate of the refrigerant is 0.05 kg/s, the rate of heat rejection to the environment is kW.
Given data:
At P = 0.14 MPa, h = 236.04 kJ/kg, s=0.9322 kJ/kg-K
At P = 0.8 MPa, h = 272.05 kJ/kg (superheated vapour)
At P = 0.8MPa, h = 93.42 kJ/kg (saturated liquid)

Question 14

A reversible cycle receives 40 kJ of heat from one heat source at a temperature of 127 ℃ and 37 kJ from another heat source at 97 ℃. The heat rejected (in kJ) to the heat sink at 47 ℃is _________.

Question 15

Figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at 0 and a mass m at end P. The natural frequency of vibration of the system is

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