The small and large pistons of an ideal hydraulic machine have areas 10 cm² and 250 cm², respectively. If the small piston is pushed downward through 50 cm, through what distance does the large piston rise?
Options

Question

The small and large pistons of an ideal hydraulic machine have areas 10 cm² and 250 cm², respectively. If the small piston is pushed downward through 50 cm, through what distance does the large piston rise?

Options

G1 Physics · Accepted Answer

For an incompressible liquid, the volume displaced by the small piston equals the volume gained below the large piston: A₁x₁ = A₂x₂. Hence, x₂ = A₁x₁/A₂. Substitute A₁ = 10 cm², x₁ = 50 cm, A₂ = 250 cm². Therefore, x₂ = 10×50/250 = 2 cm. Correct option: B.