GATE ME topic:solid-mechanics PYQs & Answers — Page 4

Questions 31–40 of 90. Imported answers require independent review unless marked reviewed.

A shaft of length

is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is

and the external diameter of the rim is

, as shown in the figure. The modulus of rigidity of the core and rim materials are

and

, respectively. It is given that

and

. When the shaft is twisted by application of a torque along the shaft axis, the maximum shear stress developed in the outer rim and the inner core turn out to be

and

, respectively. All the deformations are in the elastic range and stress-strain relations are linear. Then the ratio

is _____ (round off to 2 decimal places).

Diagram for Mechanical Engineering question 50

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A rigid beam AD of length

m is hinged at frictionless pin joint A and supported by two strings as shown in the figure. String BC passes over two small frictionless pulleys of negligible radii. All the strings are made of the same material and have equal cross-sectional area. A force

kN is applied at C and the resulting stresses in the strings are within linear elastic limit. The self-weight of the beam is negligible with respect to the applied load. Assuming small deflections, the tension developed in the string at C is ________ kN (round off to 2 decimal places).

Diagram for Mechanical Engineering question 51

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A thin-walled cylindrical pressure vessel has mean wall thickness of

and nominal radius of

. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became

. The corresponding change in the wall thickness of the cylindrical portion, i.e.

, is ________ % (round off to 3 decimal places).

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A shaft AC rotating at a constant speed carries a thin pulley of radius

m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque

about the shaft axis without causing any bending moment. The shaft is mounted on narrow frictionless bearings at A and B where AB = BC = L = 0.5 m. The taut and slack side tensions of the belt are

N and

N, respectively. The allowable shear stress for the material is 80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value of

available in the on-screen virtual calculator. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is ______ mm (round off to 2 decimal places).

Diagram for Mechanical Engineering question 53

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The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to 200 MPa stress, respectively, are

Diagram for Mechanical Engineering question 6

Your answerChoose one option.

0.01 and 0.01

0.02 and 0.01

0.01 and 0.02

0.02 and 0.02

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A cantilever beam of length,

, and flexural rigidity,

, is subjected to an end moment,

, as shown in the figure. The deflection of the beam at

Diagram for Mechanical Engineering question 17

Your answerChoose one option.

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The von Mises stress at a point in a body subjected to forces is proportional to the square root of the

Your answerChoose one option.

total strain energy per unit volume

plastic strain energy per unit volume

dilatational strain energy per unit volume

distortional strain energy per unit volume

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A prismatic bar

is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are

Diagram for Mechanical Engineering question 18

Your answerChoose one option.

and

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A column with one end fixed and one end free has a critical buckling load of 100 N. For the same column, if the free end is replaced with a pinned end then the critical buckling load will be ______ N (round off to the nearest integer).

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A steel cubic block of side 200 mm is subjected to hydrostatic pressure of 250 N/mm². The elastic modulus is

N/mm² and Poisson ratio is 0.3 for steel. The side of the block is reduced by ______ mm (round off to two decimal places).

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GATE ME topic:solid-mechanics PYQs

Question 50

Question 51

Question 52

Question 53

Question 6

Question 17

Question 17

Question 18

Question 24

Question 25