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

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A$$. the ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

The compound shaft shown is built-in at the two ends. It is subjected to a twisting moment $$T$$ at the middle. What is the ratio of the reaction torques $${{T_1}}$$ and $${{T_2}}$$ at the ends?

A circular rod of diameter $$d$$ and length $$3d$$ is subjected to a compressive force $$F$$ acting at the top point as shown below. Calculate the stress at the bottom-most support point A.