In a particular mold design, the down sprue has an area of Cross section of $$6.45\,\,c{m^2}$$ where the pouring basin leads into the sprue. The sprue is $$20$$ $$cm$$ long. The required metal flow rate at the top section of the sprue is $$820$$ $$c{m^3}/s.$$ Determine the pouring height necessary above the sprue top. Also determine the area of $$C.S$$ of sprue at its bottom to avoid the aspiration of liquid molten metal.

Which of the following materials requires the largest shrinkage allowance, while making a pattern for casting?

Consider the system of two wagons shown in Figure. The natural frequencies of this system are

A planetary gear train is shown in Figure. Internal gear (1) has 104 teeth and is held fixed and planet gear (2) has 96 teeth. How much does the planet gear rotate for sixty revolutions of the planet carrier (3) in clockwise direction?