Two cylindrical vessels fitted with pistons A and B of area of cross section 8 cm ² and 320 cm ² respectively, are joined at their bottom by a tube and they are completely filled with water. When a mass of 4 kg is placed on piston A, find : (i) the pressure on piston A, (ii) the pressure on piston B, and (iii) the thrust on piston B.

(i) As we know,

Pressure (P) = $\dfrac{\text {Thrust (F)}}{\text {Area (A)}}$

Given,

Force on the narrow piston A = 4 kg

A_A = 8 cm ²

A_B = 320 cm ²

Substituting the values in the formula above, we get,

$P_A = \dfrac{4}{8} \\[0.5em] \Rightarrow P = 0.5 \text { kg cm}^{-2} \\[0.5em]$

Hence, P_A = 0.5 kg cm^-2

(ii) As we know, by the principle of hydraulic machine

Pressure on piston A = pressure on piston B

Hence, P_B = 0.5 kg cm^-2

(iii) Thrust on piston B is acting in the upward direction, which is given by

Pressure (P) = $\dfrac{\text {Thrust (F)}}{\text {Area (A)}}$

Substituting the values, we get,

$0.5 = \dfrac{\text{thrust}}{320} \\[0.5em] \Rightarrow \text{thrust} = 0.5 \times 320 \\[0.5em] \Rightarrow \text{thrust} = 160 \text{kgf} \\[0.5em]$

Hence, thrust on piston B = 160 kgf