Question

consider a situation 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)

$\frac{2}{3}$ cm

As water is considered to be incompressible, so volume covered by inward movement of smaller piston = volume covered by outward movement of larger piston.
$L_1{A}_1=L_2{A}_2$

$L_2=\frac{A_1}{A_2}{L}_1=\frac{\pi (D_1/2{)}^2}{\pi (D_2/2{)}^2}{L}_1$

$={\left(\frac{D_1}{D_2}\right)}^2{L}_1$

$={\left(\frac{1cm}{3cm}\right)}^2\times 6cm=\frac{6}{9}cm=\frac{2}{3}cm$