A hollow shaft of $$1$$ m length is designed to transmit a power of $$30$$ kW at $$700$$ rpm. The maximum permissible angle of twist in the shaft is $${1^0}.$$ The inner diameter of the shaft is $$0.7$$ times the outer diameter. The modulus of rigidity is $$80$$ GPa. The outside diameter (in mm) of the shaft is _______

A rod is subjected to an uniaxial load within linear elastic limit. When the change in the stress is $$200$$ MPa, the change in the strain is $$0.001.$$ If the Poisson's ratio of the rod is $$0.3$$ the modulus of rigidity (in GPa) is ________ .

In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, the maximum acceleration of the slider (in m/s²) is _________

The number of degrees of freedom of the planetary gear train shown in the figure is