A band brake having band-width of $$80mm,$$ drum diameter of $$250mm,$$ coefficient of friction of $$0.25$$ and angle of wrap of $$270$$ degrees is required to exert a friction torque of $$1000N$$-$$m$$. The maximum tension (in $$kN$$) developed in the band is

In a shear cutting operation, a sheet of $$5mm$$ thickness is cut along a length of $$200mm.$$ The cutting blade is $$400mm$$ long and zero-shear $$(S=0)$$ is provided on the edge. The ultimate shear strength of the sheet is $$100$$ $$MPa$$ and penetration to thickness ratio is $$0.2.$$ Neglect friction

Assuming force $$Vs$$ displacement curve to be rectangular, the work done in $$J$$ is

In a gating system, the ratio $$1:2:4$$ represents

For the case of molding, it is decided to replace a spherical riser of diameter $$100$$ $$mm$$ by a cylindrical riser. Determine size of the cylindrical riser that will have the identical solidification time. Assume blind risering & ratio of height to radius of cylinder is $$2.$$