Twenty degree full depth involute profiled $$19$$-tooth pinion and $$37$$-tooth gear are in mesh. If the module is $$5mm,$$ the center distance between the gear pair will be

A disk clutch is required to transmit $$5$$ $$kW$$ at $$2000$$ $$rpm$$ the disk has a friction lining with Coefficient of friction equal to $$0.25.$$ Bore radius of friction lining is equal to $$25mm.$$ Assume uniform contact pressure of $$1MPa.$$ The value of outside radius of the friction lining is

A $$4$$ $$mm$$ thick sheet is rolled with $$300$$ $$mm$$ diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is $$0.1.$$ The minimum possible thickness of the sheet that can be produced in a single pass is

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