Q$1.$ Consider a $02-$series single$-$row deep$-$groove ball bearing with a $65-mm$ bore $($refer to the appendices for details$).$ The bearing experiences a $3$ kN axial load and a $7$ kN radial load, while the outer ring rotates at a speed of $500$ revolutions per minute.

$($a$)$ Calculate the equivalent radial load acting on the bearing.

$($b$)$ Assess whether the selected bearing can reliably handle this load for $10,000$ hours with a $95\%$ reliability target.

Table A$2$:Table A$1$Equivalent Radial Load Factors for Ball BearingsLoad Ratings for Single$-$Row $02-$Series Bearings.ShoulderManufacturerRating Life,Table A$3$: Typical Weibull Parameters for Two Manufacturers$90(10)1(10)$F$/$VE$)>$eLoad Ratings,$0\mathrm{.}02$Deep GrooveNeibull ParametersRating Lives$1\mathrm{.}51\mathrm{.}483$aler Cant