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

• A. 30 N
• B. 60 N
• C. 90 N
• D. 100 N

Answer 1

Answer: (C)

90 N

Since pressure is transmitted undiminished throughout the water
$\therefore \frac{F_1}{A_1}=\frac{F_2}{A_2}$
where $F_1$ and $F_2$ are the forces on the smaller and on the larger pistons respectively and $A_1$ and $A_2$ are the respective areas.
$\therefore F_2=\frac{A_2}{A_1}{F}_1=\frac{\pi (D_2/2{)}^2}{\pi (D_1/2{)}^2}{F}_1={\left(\frac{D_2}{D_1}\right)}^2{F}_1$
$=\frac{(3\times {10}^{-2}m{)}^2}{(1\times {10}^{-2}m{)}^2}\times 10N=90N$