Question

Two cylindrical vessels fitted with pistons A and B of areas of cross section $8{\text{cm}}^2$ and $400{\text{cm}}^2$ respectively, are joined together using a tube at their bottoms. The cavity is then filled with water completely. Which of the following statements are true, if a mass of $2.5\text{kg}$ is placed on the piston A?

• A. The pressure acting on the piston A = $3,125{\text{kgf m}}^{-2}$
• B. The pressure acting on the piston B = $3,125{\text{kgf m}}^{-2}$
• C. The pressure acting on the piston A = $15,625{\text{kgf m}}^{-2}$
• D. The thrust acting on the piston B = $125\text{kgf}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A The pressure acting on the piston A = $3,125{\text{kgf m}}^{-2}$
B The pressure acting on the piston B = $3,125{\text{kgf m}}^{-2}$
D The thrust acting on the piston B = $125\text{kgf}$

Given:
The area of cross section of the piston A, ${\text{A}}_1=8{\text{cm}}^2$
The area of cross section of the piston B, ${\text{A}}_2=400{\text{cm}}^2$
The mass put on the piston A = $2.5\text{kg}⟹$ Force acting on the piston A, ${\text{F}}_1\approx 2.5\text{kgf}$ ($\because 1\text{kg}\approx 1\text{kgf}$)

The pressure acting on the piston A, ${\text{P}}_1=\frac{{\text{F}}_1}{{\text{A}}_1}=\frac{2.5}{8}=0.3125{\text{kgf cm}}^{-2}$$⟹{\text{P}}_1=3,125{\text{kgf m}}^{-2}$

According to Pascal's law, this pressure will be transmitted equally and undiminished in all directions in the liquid, i.e. the pressure acting on the piston B would also be equal to $3,125{\text{kgf m}}^{-2}$.
$⟹$ Thrust acting on the piston B = $3125\times 400\times {10}^{-4}=125\text{kgf}$