GATE XE purpose:exam-prep PYQs & Answers — Page 133

Questions 1321–1330 of 1772. Imported answers require independent review unless marked reviewed.

The state of stress at a point in a body under plane stress condition is given as σ_x = 5 MPa, σ_y = −1 MPa and τ_xy = 4 MPa. If one of the principal stresses at that point is 7 MPa, then the other non-zero principal stress (in MPa) is _____

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A massless rod of length L having a concentrated mass m attached at its mid-point is held at rest between the smooth ground and the smooth wall when it makes an acute angle θ₀ with the ground as shown. The rod is then released. The acceleration due to gravity is g. At an instant when the angle between the rod and ground is θ, the velocity of the mass m is

Diagram for Engineering Sciences question 10

Your answerChoose one option.

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A cantilever beam of constant cross section is subjected to a positive moment

and a positive axial force

as shown. The normal stress due to the axial force

is 200 MPa and the maximum compressive stress due to the moment

is 100 MPa. If the point A is located on the top surface and the point B is located on the centroidal axis of the beam, the stress elements at these points are (with stresses shown in MPa)

Diagram for Engineering Sciences question 11

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Diagram for Engineering Sciences question 11 (figure 2)

Diagram for Engineering Sciences question 11 (figure 3)

Diagram for Engineering Sciences question 11 (figure 4)

Diagram for Engineering Sciences question 11 (figure 5)

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The block of mass m = 10 kg is held in place along the incline by the force F applied via a pulley arrangement as shown. The coefficient of static friction between the block and incline is 0.65. The range of F (in N) for which the block will remain at rest is (use acceleration due to gravity g = 10 m/s²)

Diagram for Engineering Sciences question 12

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6.3 to 106.30

0 to 106.30

0 to 53.15

53.15 to 106.30

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The frame shown comprises members ABC, BE, BF, and DEF. It is pin supported at A and D. Members BE and BF are pin connected to ABC and DEF. The vertical load P is applied at C. The force in the member BF is

Diagram for Engineering Sciences question 13

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compressive P

tensile P

compressive 2P

tensile 2P

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A simply supported beam is subjected to a concentrated force P = 4800 N at the mid-span as shown. The flexural rigidity of the beam is EI = 11 × 10⁶ N·m². The curvature of the beam between points Q and R is given as κ = (Px/2EI). The magnitude of deflection (in mm) of the beam at x = 0.5 m is

Diagram for Engineering Sciences question 14

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0.5

1.0

1.5

2.0

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The shear force (V) diagram for a cantilever beam under certain loads applied at points B and C is shown.

Diagram for Engineering Sciences question 15

The magnitude of applied force at B (F_B), and the magnitude of applied force at C (F_C), are

Your answerChoose one option.

F_B = 500 N, F_C = 300 N

F_B = 200 N, F_C = 300 N

F_B = 300 N, F_C = 200 N

F_B = 300 N, F_C = 500 N

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A bar of length 1 m, having a uniform area of cross section 1000 mm², is fixed at one end and subjected to a uniaxial tensile load of 200 kN at the other end. Along with the tensile load, the rod also experiences a uniform temperature rise ΔT = 100 °C. The material of the rod has a Young’s modulus E = 200 GPa and coefficient of thermal expansion α = 1×10⁻⁵/°C. The elongation of the rod (in mm) is ________.

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A solid rod, with uniform circular cross section, of length 100 mm and diameter 100 mm is subjected to a uniaxial tensile load. As a result, the increase in length of the rod is observed to be 1 mm while the reduction in diameter of the rod is observed to be 0.03 mm. If the Young’s modulus of the material of the rod is 260 GPa, the shear modulus (in GPa) of the material of the rod is ________.

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A spherical pressure vessel has inner diameter of 4 m and wall thickness of 10 mm. It is made of a steel having tensile yield strength of 200 MPa. Neglecting radial stress and using the maximum shear stress theory, the maximum value of gauge pressure (in MPa) that the wall of the pressure vessel can withstand is ________ (rounded off to two decimal places).

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GATE XE purpose:exam-prep PYQs

Question 9

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Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18