A spur pinion of pitch diameter $$50$$ $$mm$$ rotates at $$200$$ $$rad/s$$ and transmits $$3$$ $$kW$$ power. The pressure angle of the tooth of the pinion is $${20^ \circ }$$. Assuming that only one pair of the teeth is in contact , the total force (in Newton ) exerted by a tooth of the pinion on the tooth on a mating gear is _________

With respect to metal working, match Group A with Group B:

The relationship between true strain $$\left( {{\varepsilon _T}} \right)$$ and engineering strain $$\left( {{\varepsilon _E}} \right)$$ in a uniaxial tension test is given as

A mild steel plate has to be rolled in one pass such that the final plate thickness is $$2/{3^{rd}}$$ of the initial thickness, with the entrance speed of $$10m/min$$ and roll diameter of $$500mm.$$ If the plate widens by $$2\% $$ during rolling, the exit velocity (in $$m/min$$) is ____________