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 $$2.$$

Two steel bars each of diameter $$10mm$$ are coaxially friction welded end to end at an axial pressure of $$200MPa$$ and rotational speed of $$400rpm$$. The coefficient of friction between the mating faces of the rotating bars is $$0.50.$$ The torque is assumed to act at the $$3/{4^{th}}$$ radius of the rotating bar. The power (in $$kW$$) consumed at the interface of the welding is