Question

Consider two syringes with diameters of the smaller piston and larger piston being $1 \, cm$ and $3\,cm$ respectively, excluding needle. Both are filled with water and are connected with a tightly fitted rubber tube filled with water. Now, if a force of $10\,N$ is applied to the smaller piston, then what is the force exerted on the larger piston?

• A. $30 \, N$
• B. $60 \, N$
• C. $90 \, N$
• D. $100 \, N$

Answer 1

Answer: (C)

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.
$\therefore F_{2} \, =\frac{A_{2}}{A_{1}}F_{1}=\frac{\pi \left(\right. D_{2} / 2 \left.\right)^{2}}{\pi \left(\right. D_{1} / 2 \left.\right)^{2}}F_{1}=\left(\frac{D_{2}}{D_{1}}\right)^{2}F_{1}$
$=\frac{\left(\right. 3 \times \left(10\right)^{- 2} m \left.\right)^{2}}{\left(\right. 1 \times \left(10\right)^{- 2} m \left.\right)^{2}}\times 10\,N=90\,N$