A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter of $$10$$ $$mm$$ diameter between points $$(0, 0)$$ and $$(100, 100)$$ on the $$XY$$ plane (dimensions in $$mm$$). The feed rate used for milling is $$50$$ $$mm/min.$$ Milling time for the slot (in seconds) 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