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

A taper hole is inspected using a $$CMM,$$ with a probe of $$2mm$$ diameter. At a height, $$Z=10mm$$ from the bottom, $$5$$ points are touched and a diameter of circle (not compensated for probe size) is obtained as $$20mm.$$ similarly, a $$40mm$$ diameter is btained at a height $$Z=40mm.$$ The smaller diameter (in $$mm$$) of hole at $$Z=0$$ is

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 $$2.$$

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