GATE XE year:2025 PYQs & Answers — Page 9

Questions 81–90 of 175. Imported answers require independent review unless marked reviewed.

The figure shows the stress distribution across an internal surface of a rectangular beam of height 30 mm and depth 10 mm. The normal stress distribution is given by the expression

; y is the distance in mm from the centroidal axis of the beam. Assume that there is no variation in the stress distribution along the z-direction. Which of the following statements is/are CORRECT?

Diagram for Engineering Sciences question 81

Your answerSelect all correct options. You can choose more than one.

The net force in the x direction is 150 kN.

The net force in the x direction is 75 kN.

The net moment about the z axis is 4500 Nm.

The net moment about the z axis is 2250 Nm.

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A vertical column fixed at one end is subjected to a compressive axial load at the free end. The column’s section modulus, EI, is

and the cross-section area is

. The length of the column is 2 m. The yield stress of the material is 145 MPa. If the column can fail either in buckling or by Tresca’s criterion, the maximum load that the structure can safely sustain is ____ kN (rounded off to one decimal place).

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A simply-supported beam, with a point load P = 150 kN at a distance of L/3 from the left end, is shown in the figure. The elastic-strain energy (U) of the beam is given by the following expression:

where the section modulus, EI, is 16.66 × 10⁵ Nm² and the length of the beam L is 1 m. The deflection at the loading point is ____ mm (rounded off to two decimal places).

Diagram for Engineering Sciences question 83

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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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GATE XE year:2025 PYQs

Question 81

Question 82

Question 83

Question 84

Question 85

Question 86

Question 87

Question 88

Question 89

Question 90