GATE XE topic:applied-science PYQs & Answers — Page 29

Questions 281–290 of 1772. Imported answers require independent review unless marked reviewed.

A simply-supported beam has a circular cross-section with a diameter of 20 mm, area of 314.2 mm², area moment of inertia of 7854 mm⁴ and a length L of 4 m. A point load P = 100 N acts at the center and an axial load Q = 20 kN acts through the centroidal axis as shown in the figure. The magnitude of the offset between the neutral axis and the centroidal axis, at L/2 from the left, is __________ mm (rounded off to one decimal place).

Diagram for Engineering Sciences question 84

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A massless cantilever beam, with a tip mass m of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length L = 1 m, with a circular cross-section of diameter d = 20 mm. The Young’s modulus of the beam material is 200 GPa. The natural frequency of the spring-mass system is ____ Hz (rounded off to two decimal places).

Diagram for Engineering Sciences question 85

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An electric motor’s rotor is spinning at 1500 rpm when its load and power are cut-off. The rotor which has a mass of 50 kg and a radius of gyration of 200 mm, then coasts down to rest. Due to kinetic friction, a constant torque of 10 Nm acts on the rotor as it coasts down. The number of revolutions executed by the rotor before it comes to rest is ____ (in integer).

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A bar of length L = 1 m is fixed at one end. Before heating its free end has a gap of δ = 0.1 mm from a rigid wall as shown in the figure. Now the bar is heated resulting in a uniform temperature rise of 10 °C. The coefficient of linear thermal expansion of the material is 20 × 10⁻⁶ /°C and the Young’s modulus of elasticity is 100 GPa. Assume that the material properties do not change with temperature. The magnitude of the resulting axial stress on the bar is ____ MPa (in integer).

Diagram for Engineering Sciences question 87

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A tank is divided into two compartments with one compartment containing a gas at a given pressure, while the second is completely evacuated. If the partition is removed, the gas occupies the entire compartment. Which one of the following statements is CORRECT?

Your answerChoose one option.

Work done is equal to the area under the curve of a p–V diagram

Expansion of gas is not restrained by external force

The entire process is reversible

The overall change in volume is zero for the entire system

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A cylinder of volume 0.1 m³ is filled with nitrogen at 10 MPa and 300 K. Consider nitrogen to be an ideal gas. The cylinder develops a leak and nitrogen escapes to atmosphere which is at 0.1 MPa. After some time, the pressure in the cylinder reduces to 5 MPa. Assuming the cylinder and the leaked gas temperature remains constant at 300 K, the work done (in MJ) by nitrogen gas is

Your answerChoose one option.

0.1

0.5

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A closed system undergoes a process 1–2 in which it absorbs 150 kJ of energy as heat and does 90 kJ of work. Then it follows another process 2–3 in which 80 kJ of work is done on it while it rejects 60 kJ as heat. If it is desired to restore the system to the initial state (state 1) by an adiabatic path, the work interaction (in kJ) in this process will be

Your answerChoose one option.

100

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The inlet and outlet temperatures of the flowing fluid during a steady state flow process are the same as that of the surroundings. If the changes in kinetic and potential energies are neglected, the maximum power that can be obtained is equal to

Your answerChoose one option.

the rate of increase in enthalpy of the flowing fluid

the rate of decrease in Helmholtz energy of the flowing fluid

the rate of decrease in Gibbs free energy of the flowing fluid

the rate of decrease in internal energy of the flowing fluid

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refers to the ratio of specific heats, the air-standard efficiency of an Otto cycle is

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Let

and

denote the absolute temperatures of high and low temperature reservoirs, respectively. The coefficient of performance of a reversible refrigerator operating between these two reservoirs is

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GATE XE topic:applied-science PYQs

Question 84

Question 85

Question 86

Question 87

Question 88

Question 89

Question 90

Question 91

Question 92

Question 93