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 $1 \,cm$ and $3\, cm$ respectively. If a force of $10\, N$ is applied to the smaller piston then the force exerted on the larger piston is , if the smaller piston is pushed in through $6 \,cm$, 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
$L_{1}A_{1}=L_{2}A_{2}$
$L_{2}=\frac{A_{1}}{A_{2}} L_{1} = \frac{\pi\left(D_{1} /2\right)^{2}}{\pi\left(D_{2} /2\right)^{2}} L_{1}= \left(\frac{D_{1}}{D_{2}}\right)^{2} L_{1}$
$=\left(\frac{1\, cm}{3 \, cm}\right)^{2} \times 6 \, cm =\frac{6}{9} cm$
$=\frac{2}{3}\, cm$