GATE XE Mechanics of deformable bodies PYQs & Answers

Questions 1–10 of 133. Imported answers require independent review unless marked reviewed.

Two axial members, namely OP and OQ, are pin joined at O as shown in the figure. A force

acts at point P along the positive x direction and a force

acts at point Q along the positive y direction.

The resultant of the applied forces makes an angle

(anticlockwise from the positive x-axis).

The value of

is _____.

Diagram for Engineering Sciences question 66

Your answerChoose one option.

30°

45°

60°

75°

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Two smooth drums each weighing

and radius,

are connected by a stiff rope of length,

as shown in the figure. Force

is applied using a massless lever (RS) of length,

. The friction between the drums and the lever (RS) is negligible. The system is in static equilibrium.

Which one of the following represents the CORRECT free body diagram of the lever (RS)?

Figures are not to scale.

, and

in the options are reaction forces and

is the frictional force.

Diagram for Engineering Sciences question 67

Your answerChoose one option.

Diagram for Engineering Sciences question 67 (figure 2)

Diagram for Engineering Sciences question 67 (figure 3)

Diagram for Engineering Sciences question 67 (figure 4)

Diagram for Engineering Sciences question 67 (figure 5)

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Which among the following options is/are CORRECT unit(s) of stress?

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

N/m

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A 2D state of stress at a point in a body is given by

MPa,

MPa and

MPa.

The radius of the Mohr’s circle for the given state of stress is _____ MPa (rounded off to two decimal places).

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Sum of the principal stresses of a 2D stress state

is _____ (in integer).

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One column with square cross section of side

and another column with rectangular cross section of breadth

and width

(

) are made from the same material. Both the columns have one end fixed, and the other end is free. They are subjected to axial loads along the centroidal axis.

Consider the area of cross sections of both the columns to be the same. The minimum critical Euler buckling loads of the columns with rectangular and square cross-sections are

and

, respectively.

Then

is _____.

Your answerChoose one option.

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Two prismatic rods of identical lengths are designed for the same strain energy density when subjected to the same axial load. One of the rods is made of steel (Young’s modulus = 210 GPa) and the other is made of aluminum (Young’s modulus = 70 GPa).

If the diameter of the aluminum rod is 70 mm, then which one of the following options corresponds to the diameter of the steel rod in mm?

Your answerChoose one option.

53.19

210

29.13

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A 2D stress state of pure shear is shown in the figure.

Diagram for Engineering Sciences question 80

Which one of the following options is equivalent to the given stress state?

Figures are not to scale.

Your answerChoose one option.

Diagram for Engineering Sciences question 80 (figure 2)

Diagram for Engineering Sciences question 80 (figure 3)

Diagram for Engineering Sciences question 80 (figure 4)

Diagram for Engineering Sciences question 80 (figure 5)

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The bending moment diagram for a simply supported beam is piecewise linear as shown in the figure. The bending moment

m is 5 Nm. The beam has a rectangular cross-section with an area of 1 m

The absolute value of the maximum shear stress on the cross-section at

m is _____ N/m

(in integer).

Diagram for Engineering Sciences question 83

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A thin walled cylindrical container of diameter 2 m and wall thickness of 2.5 cm is made of steel whose Young’s modulus is 200 GPa and yield stress is 450 MPa.

Using von Mises criteria, the maximum possible pressure is _____MPa (rounded off to the nearest integer).

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GATE XE Mechanics of deformable bodies PYQs

How to practice Mechanics of deformable bodies

Question 66

Question 67

Question 70

Question 73

Question 74

Question 77

Question 78

Question 80

Question 83

Question 84