In a hydraulic lift, the small piston has an area of $5\ \text{cm}^2$ and the large piston an area of $500\ \text{cm}^2$. A car of mass $1000\ \text{kg}$ sits on the large piston, as shown in the figure. Taking $g = 10\ \text{m/s}^2$, the force needed on the small piston to hold the car up, and how far that piston must move to raise the car by $1\ \text{cm}$, are

Fig. 1: A hydraulic lift: a narrow piston of area 5 square centimetres pushed down by a force F, joined by liquid to a wide piston of area 500 square centimetres carrying a 1000 kg car.