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 I cm and 3 cm respectively. If the smaller piston is pushed in through 6 cm, how much does the longer piston move out?

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$\frac{3}{2} cm$

$\frac{1}{3} cm$

$\frac{2}{3} cm$

$\frac{1}{2} cm$

answer is A.

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Detailed Solution

As water is considered to be incompressible, so volume covered by inward movement of smaller piston = volume covered by outward movement of larger piston.

$L_{1} A_{1} = L_{2} A_{2}$

$L_{2} = \frac{A_{1}}{A_{2}} L_{1} = \frac{π {(\frac{D_{1}}{2})}^{2}}{π {(\frac{D_{2}}{2})}^{2}} L_{1} = {(\frac{D_{1}}{D_{2}})}^{2} L_{1}$

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

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