A $12,000-$N car is raised using a hydraulic lift, which consists of a U$-$tube with arms of unequal areas, filled with incompressible oil and capped at both ends with tight$-$fitting pistons. The wider arm of the U$-$tube has a radius of and the narrower arm has a radius of $.$ The car rests on the piston on the wider arm of the U$-$tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? $($For purposes of this problem, you can neglect the weight of the pistons.$)$