Previous Year Problems in Mechanics

A free bar of length 1 is uniformly heated form 0°C to a temperature t°C. α is the coefficient of linear expansion and E the modulus of elasticity. The stress in the bar is

• αtE/2

• αtE

• Zero

• None of the above

Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rod is made of mild steel having the modulus of elasticity of 206 GPa. The other rod is made of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?

• Both rods elongate by the same amount

• Mild Steel rod elongates more than Cast Iron rod

• Cast Iron rod elongates more than Mild Steel rod

• As the stresses are equal, strains are also equal

A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by σ, and a respectively, then

• σ, = 0,0₂ = 0

• 0,0,0,0

• σ, = 0,0₂ ≠0

• σ, ≠0,0₂ ≠0

A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of AT. The Young's modulus is E and the coefficient of linear expansion is a. The thermal stress in the rod is

• 0

• αAT

• ΕαΔΤ

• EαATL

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young's modulus of the material varies linearly from E, to E, along the length of the rod, the normal stress developed at the section -

• P/A

• P(E1-E2)/A(E1+(E2)

• PE2/AE1

• PE1/AE2

A circular rod of length L and area of cross-section A has a modulus of elasticity E and coefficient of thermal expansion a. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by AT, then

• stress developed in the rod is EaAT and strain developed in the rod is aAT

• Pal

• Pal

• T₁ = (²+²) -²3 (²+8²)T₂ ==