In a sand casting operation, the total liquid head is maintained constant such that it is equal to the mould height. The time taken to fill the mould with a top gate is $${t_A}.$$ If the same mould is filed with a bottom gate, then the time taken is $${t_B}.$$ Ignore the time required to fill the runner and frictional effects. Assume atmospheric pressure at the top molten metal surfaces. The relation between the $${t_A}$$ and $${t_B}$$ is

Match List - $${\rm I}$$ (products) with List - $${\rm II}$$ (casting process) and select the correct answer using the codes given below the lists

A mould has a downsprue whose length is $$20$$ $$cm$$ and the cross sectional area at the base of the down sprue is $$1\,\,c{m^2}.$$ The down sprue feeds a horizontal runner leading into the mould cavity of volume $$1000\,\,c{m^3}.$$ The time required to fill the mould cavity will be

Gray cast iron blocks $$200 \times 100 \times 10\,\,mm$$ are to be cast in sand moulds. Shrinkage allowance for pattern making is $$1$$%. The ratio of the volume of pattern to that of the casting will be