Question

Two syringes of different cross-sections (without needles) filled with water are connected with tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are 1.0cm and 3.0cm respectively
(i) Find the force exerted on the larger piston when a force of 10N is applied to the smaller piston.
(ii) If the smaller piston is pushed in through 6.0cm, how much does the larger piston move out?

Answer 1

Dear Student

a. Pressure is undiminished under transformation
$$\begin{gathered} F_2=\frac{A_2}{A_1}{F}_1=\frac{\pi (3/2x{10}^{-2}m{)}^2}{\pi (1/2x{10}^{-2}m{)}^2}\times 10N \\ {F}_2=90N \end{gathered}$$

b. Water is considered to be perfectly incompressible. Volume covered by the movement of smaller piston inwards is equal to volume moved outwards due to the larger piston

$$\begin{gathered} L_1{A}_1=L_2{A}_2 \\ {L}_2=\frac{A_1}{A_2}{L}_1=\frac{\pi (1/2x{10}^{-2}m{)}^2}{\pi (3/2x{10}^{-2}m{)}^2}\times 6\times {10}^{-2}m \\ {L}_2=0.67\times {10}^{-2}m \end{gathered}$$

atmospheric pressure is common to both pistons and has been ignored

regards