Question

Two syringes of different cross section (without needle) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are $1cm$ and $3cm$ respectively. If a force of $10N$ is applied to the smaller piston then the force exerted on the larger piston is , if the smaller piston is pushed in through $6cm$, how much does the longer piston move out?

• A. $\frac{2}{3}cm$
• B. $\frac{3}{2}cm$
• C. $\frac{1}{3}cm$
• D. $\frac{1}{2}cm$

Answer 1

Answer: (A)

As water is considered to be incompressible, so volume covered by inward movement of smaller piston = volume covered by outward movement of larger piston
$L_1{A}_1=L_2{A}_2$
$L_2=\frac{A_1}{A_2}{L}_1=\frac{\pi {\left(D_1/2\right)}^2}{\pi {\left(D_2/2\right)}^2}{L}_1={\left(\frac{D_1}{D_2}\right)}^2{L}_1$
$={\left(\frac{1cm}{3cm}\right)}^2\times 6cm=\frac{6}{9}cm$
$=\frac{2}{3}cm$