The diameters of a set of connected pistons are 6.0 mm and 24 mm. If a 2.0-kg mass is placed on the smaller piston and the piston is displaced 5.0 mm, the distance the second piston moves is
A) 0.31 mm.
B) 5.0 mm.
C) 1.3 mm.
D) Hold on; not enough information is given.

Question

Quizplus · Accepted Answer

The principle of hydraulic systems, which these pistons are a part of, dictates that the force applied on one piston is transferred to the other piston but the distances moved are inversely proportional to the areas of the pistons. Since the area is proportional to the square of the diameter, the second piston moves a smaller distance. The ratio of the diameters squared gives the inverse ratio of the distances moved. So, $(6/24)^2 = (1/4)^2 = 1/16$, and since the smaller piston moves 5.0 mm, the larger piston moves $5.0 mm / 16 = 0.3125 mm$, which rounds to 0.31 mm.

The Diameters of a Set of Connected Pistons Are 6