A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is $$1$$ unit. Radius of the Mohr's circle, characterizing the state at that point, is

A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It further subjected to a torque of 10 KN-m. The maximum principal stress experienced on the shaft is closest to

For the component loaded with a force $$F$$ as shown in the figure, the axial stress at the corner point $$P$$ is

A compression spring is made of music wire of $$20$$ mm diameter having a shear strength and shear modulus of $$800$$ MPa and $$80$$ GPa respectively. The mean coil diameter is $$20$$ mm, free length is $$40$$ mm and the number of active coils is $$10.$$ If the mean coil diameter is reduced to $$10$$ mm, the stiffness of the spring is approximately