A torque of $$10$$ $$N-m$$ is transmitted through a stepped shaft as shown in figure. The torsional stiffnesses of individual sections of lengths $$MN, NO$$ and $$OP$$ are $$20$$ $$N-m/rad,$$ $$30$$ $$N-m/rad$$ and $$60$$ $$N-m/rad$$ respectively. The angular deflection between the ends $$M$$ and $$P$$ of the shaft is

The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the $$x$$ and $$y$$ directions are $$100$$ MPa and $$20$$ MPa respectively. The radius of Mohr's stress circle representing this state of stress is

The figure below shows a steel rod of $$25$$ mm² cross sectional area. It is loaded at four points, K, L, M and N. Assume E_steel $$=$$ $$200$$ GPa. The total change in length of the rod due to loading is

In terms of Poisson's ratio $$\left( \mu \right)$$ the ratio of Young's Modulus $$(E)$$ to Shear Modulus $$(G)$$ of elastic materials is