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 __________.

The hot tearing in a metal casting is due to

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

A cylindrical blind riser with diameter $$d$$ and height $$h,$$ is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio $$h:d$$ is