A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is $$100 MPa.$$ If the yield, ultimate and corrected endurance strength of the shaft material are $$300$$ $$MPa,$$ $$500$$ $$MPa$$ and $$200$$ $$MPa,$$ respectively, then the factor of safety for the shaft is __________.

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $$0.2.$$ The dimensions shown in the figure are in mm. The braking torque (in $$N.m$$) for the brake shoe is ________.

Match the casting defects (Group A) with the probable causes (Group B):

The hot tearing in a metal casting is due to