GATE Prev Year : Mechanics of Materials Test-4

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Question 1

A steel shaft ‘A’ of diameter ‘d’ and length ‘l’ is subjected to a torque ‘T’. Another shaft ‘B’ made of aluminium of the same diameter ‘d’ and length 0.5 l is also subjected to the same torque ‘T’. The shear modulus of steel is 2.5 times the shear modulus of aluminium. The shear stress in the steel shaft is 100 MPa. The shear stress in the aluminium shaft, in MPa, is

• A40
• B50
• C100
• D250

Question 2

Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have

• Aequal deflections but not equal slopes
• Bequal slopes but not equal deflections
• Cequal slopes as well as equal deflections
• Dneither equal slopes nor equal deflections

Question 3

Two helical tensile Springs of the same material and also having identical mean coil diameter and weight, have wire diameters d and d/2. The ratio of their stiffness is

• A1
• B4
• C64
• D128

Question 4

The ratio of Euler’s buckling loads of columns with the same parameters having (i) both ends fixed, and (ii) both ends hinged is

• A2
• B4
• C6
• D8

Question 5

The stress-strain behaviour of a material is shown in figure. Its resilience and toughness, in Nm/m³, are respectively

• A
• B
• C
• D

Question 6

The relationship between Young’s modulus (E), Bulk modulus (K) and Poisson’s ratio (v) is given by

• AE = 3K(1 – 2 v)
• BK = 3E (1 – 2 v)
• CE = 3K(1 –v)
• DK = 3E (1 – v)

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