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

A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled with water upto a depth of $$2$$m and suspended along with its upper rim. The density of water is $$1000$$kg/m³ and acceleration due to gravity is $$10$$ m/s². The self weight of the cylinder is negligible. The formula for hoop stress in a thin walled cylinder can be used at all points along the height of the cylindrical container.

The axial and circumferential stress $$\left( {{\sigma _{a,}}\,{\sigma _c}} \right)$$ experienced by the cylinder wall a mid-depth ($$1$$ m as shown) are

The strain energy stored in the beam with flexural rigidity $$EI$$ and loaded as shown in the figure is

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