In an interchangeable assembly, shafts of size $${25.000^{\matrix{ { + 0.040} \cr { - 0.010} \cr } }}\,\,mm$$ mate with holes of size $${25.000^{\matrix{ { + 0.030} \cr { + 0.020} \cr } }}\,\,mm.$$

The maximum interference (in microns) in the assembly is

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $$\Delta T.$$ If the thermal coefficient of the material is $$\alpha $$, young's modulus is $$E$$ and the Poisson's ratio is $$\upsilon $$, the thermal stress developed in the cube due to heating is

A $$200$$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by $$250$$^oC. If the Young's modulus and coefficient of thermal expansion are $$200$$ GPa and $$1 \times {10^{ - 5}}/{}^ \circ C,$$ respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _________

The state of stress at a point under plane stress condition is
$${\sigma _{xx}} = 40\,$$ MPa, $${\sigma _{yy}} = 100\,$$ MPa & $${\tau _{xy}} = 40$$ MPa.
The radius of the Mohr's circle representing the given state of stress in MPa is