The diameter of a recessed ring was measured by using two spherical balls of diameter $${d_2} = 60mm$$ and $${d_1} = 40mm$$ as shown in the figure.

The distance $${H_2} = 35.55\,\,mm$$ and $${H_1} = 20.55\,\,mm$$. The diameter ($$D,$$ in $$mm$$) of the ring gauge is __________________.

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table

Consider a simply supported beam of length $$50$$h, with a rectangular cross-section of depth h, and width $$2$$h. The beam carries a vertical point load P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $${\tau _1}$$ and $${\tau _2}.$$ If $${{{R_1}} \over {{R_2}}} = 2,$$ then $${{{\tau _1}} \over {{\tau _2}}}$$ is _______.