Engineering Sciences
GATE XE exam:gate PYQs
Build your understanding with focused practice from past exam papers.
Questions 451–460 of 1772. Imported answers require independent review unless marked reviewed.
Question 79
Open questionXE-DMSQ2 marksNeeds review
A critical point on a component is subjected to the state of stress
as given in the following. The yield strength of the material is 400 MPa. By considering maximum shear stress (Tresca) theory, the possible value(s) of
at the onset of yielding is/are,
Your answerSelect all correct options. You can choose more than one.
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Open questionXE-DNAT2 marksNeeds review
A plane passing through a point Q inside a body is shown. The unit normal of the plane is
, as shown in the figure. The traction (stress) vector on the plane at point Q is given by
MPa. Given that at point Q,
, the shear stress component
(in MPa, rounded off to two decimal places) is __________ . 
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Open questionXE-DNAT2 marksNeeds review
A rigid massless bar PQ is hinged at its end P and supported through a spring of stiffness
at point Q. A vertically downward force
is applied at the free end R of the bar. If the vertical component of the displacement at R is 30 mm, then the stiffness of the spring (in kN/m, rounded off to one decimal place) is ___. 
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Open questionXE-DNAT2 marksNeeds review
A beam of rectangular cross-section, as shown in the figure, is made of two perfectly bonded layers of different materials and equal thickness. The Young’s moduli of the two materials are
and
, where
. The beam is subjected to pure bending. If
mm, the distance of the neutral plane from the top surface of the beam is ______ (in mm, rounded off to two decimal places). 
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Open questionXE-DNAT2 marksNeeds review
A stepped beam is made of a material whose Young’s modulus is E. The dimensions of the two stepped sections are such that the sectional moments of inertia,
and
, are related as
. The beam is fixed at one end and a load of F is applied at the free end as shown in the figure. Under this loading condition, if the strain energy of the stepped beam is written as
, then the value of
is ______ (rounded off to two decimal places). 
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Open questionXE-DNAT2 marksNeeds review
A cylindrical pressure vessel is constructed by bolting two symmetric halves of flanged semi-cylindrical shells. A cross-sectional view of the vessel is shown in the figure. The inner diameter of the vessel is 2 m and the length is 10 m. Each row comprises 100 bolts along the length of the vessel. If the vessel is pressurized to a net pressure of
N/m
, and assuming that the end caps of the vessel do not take any load in the radial direction, then the load borne by each bolt is __________ (in kN, rounded off to one decimal place). 
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Open questionXE-DNAT2 marksNeeds review
A turn-table is rotating about its center with an angular velocity of 2 rad/s in the counter-clockwise direction. There is a groove in the turn-table within which a marble moves with a constant speed
m/s relative to the turn-table. At a given instant, the marble is at a radial distance of 1 m from the center and the line joining the center of the turn-table with the marble makes an angle of 30° with the groove. The value of
(in m/s, rounded off to one decimal place) for which there is no radial acceleration for the marble at this instant is _____.
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Open questionXE-DNAT2 marksNeeds review
The system shown in the figure is in static equilibrium. The spring is massless and has a spring constant of K=1 kN/m. The free length of the spring is 1 m. All bodies in the system except the spring are rigid and have mass of M=1 kg. All surfaces are frictionless and pin joints are ideal. The elongation of the spring (in mm, rounded off to the nearest integer) in this configuration is _____. Take the acceleration due to gravity
m/s
.
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Open questionXE-DNAT2 marksNeeds review
A square block of side 1 m and mass 10 kg is resting on a horizontal surface. The coefficient of static friction between the block and the surface is 0.75. A horizontal force P acts on the block as shown in the figure. The force P is gradually increased from zero until the block either slides or topples. The maximum value of
(in m, rounded off to two decimal places) for which the block slides without toppling is _____. Take the acceleration due to gravity
m/s
.
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Open questionXE-EMCQ1 markNeeds review
A heat source at temperature
transfers the same amount of heat to a sink under the following situations:Case A: Sink is at temperature
Case B: Sink is at temperature
If
, which one of the following statements is TRUE?Your answerChoose one option.
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