A solid circular shaft has to transmit $150$ kW of power at $200$ rpm $.$ If the allowable shear stress is $75$ MPa and permissible twist is $1$ in a length of $3$ m $,$ find the diameter of the shaft. Take G $=82$ GPa $.$

A shaft is required to transmit $245$ kW power at $240$ rpm $.$ The maximum torque is $50\%$ more than the mean torque. The shear stress in the shaft is not to exceed $40\frac{N}{m}m2$ and the twist $1$ per meter length. Taking $G=80k\frac{N}{m}m2,$ determine the diameter required if$,$ a$.)$ the shaft is solid. b$.)$ the shaft is hollow with external diameter twice the internal diameter.

A power of $2\mathrm{.}2$MW has to be transmitted at $60r.p.m.$ If the allowable stress in the material of the shaft is $85$ MPa $,$ find the required diameter of the shaft, if it is solid. If instead, a hollow shaft is used with $3D_E=4D_1,$ calculate the percentage saving in weight per meter length of the shaft. Density of the shaft material is $7800k\frac{g}{m^3}.$