Two identical ball bearings $$P$$ and $$Q$$ are operating at loads $$30kN$$ and $$45kN$$ respectively. The ratio of the life of bearing $$P$$ to the life of bearing $$Q$$ is

A journal bearing has a shaft diameter of $$40mm$$ and a length of $$40mm.$$ The shaft is rotating at $$20$$ $$rad/s$$ and viscocity of the lubricant is $$20mPa.s.$$ The clearance is $$0.020mm.$$ The loss of the torque due to viscocity of the lubricant is approximately

A natural feed journal bearing of diameter $$50mm$$ and length $$50mm$$ operating at $$20$$ revolutions/sec carries a load of $$2kN$$. The lubricant used has a viscosity of $$20mPa$$-$$s$$. The radial clearance is $$50\mu m.$$ The Sommerfeld number for the bearings is

A ball bearing operating at a load $$F$$ has $$8000$$hours of life. The life of the bearing, in hours, when the load is doubled to $$2F$$ is