A shaft subjected to torsion experiences a pure shear stress $$\tau $$ on the surface. The maximum principal stress on the surface which is at $$45$$⁰ to the axis will have a value

A $$200 \times 100 \times 50$$ mm steel block is subjected to a hydrostatic pressure of $$15$$ MPa. The Young's modulus and Poisson's ratio of the material are 200 GPa and $$0.3$$ respectively. The change in the volume of the block in mm³ is

Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having he 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?

The circular disc shown in its plan view in the figure rotates in a plane parallel to the horizontal plane about the point $$O$$ at a uniform angular velocity $$\omega $$. Two other points $$A$$ and $$B$$ are located on the line $$OZ$$ at distances $${r_A}$$ and $${r_B}$$ from $$O$$ respectively.

The acceleration of point $$B$$ with respect to point $$A$$ is a vector of magnitude