Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A$$. the ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

For the case of a slender column of length $$l,$$ and flexural rigidity $$EI$$ built-in at its base and free at the top, the Euler’s critical buckling load is

In spur gears having involute teeth, the product of circular pitch and diametral pitch is _________

A $$1500$$ $$W$$ electrical heater is used to heat $$20$$ $$kg$$ of water $$\left( {{C_p} = 4186\,\,J/kg\,\,K} \right)$$ in an insulated bucket, from a temperature of $${30^{^0}}C$$ to $${80^{^0}}C$$. If the heater temperature is only infinitesimally larger than the water temperature during the process, the change in entropy for the heater is ________$$J/K$$ and for water _______$$J/K.$$