Question

Two cylindrical vessels fitted with pistons A and B of area of cross section $8c{m}^2$ and $320c{m}^2$ respectively, are joined at their bottom by a tube and they are completely filled with water. Find : (i) the pressure on piston A, (ii) the pressure on piston B, and (iii) the thrust on piston B.(consider effort on piston A $E=4kgf$)

• A. (i) $5$ $kgf$ $c{m}^{-2}$
  (ii) $5$ $kgf$ $c{m}^{-2}$
  (iii) $160$ $kgf$
• B. (i) $5$ $kgf$ $c{m}^{-2}$
  (ii) $5$ $kgf$ $c{m}^{-2}$
  (iii) $16$ $kgf$
• C. (i) $10$ $kgf$ $c{m}^{-2}$
  (ii) $10$ $kgf$ $c{m}^{-2}$
  (iii) $160$ $kgf$
• D. (i) $0.5$ $kgf$ $c{m}^{-2}$
  (ii) $0.5$ $kgf$ $c{m}^{-2}$
  (iii) $160$ $kgf$

Answer 1

Answer: (D)

(i) $0.5$ $kgf$ $c{m}^{-2}$

(ii) $0.5$ $kgf$ $c{m}^{-2}$
(iii) $160$ $kgf$
Let $E$ be the effort applied on the smaller piston $A$ and $L$ be the load required on the larger piston $B$.
Area of cross section of pistion $A=8c{m}^2$
Area of cross section of pistion $A=320c{m}^2$
(i) Pressure acting on piston $A$ in the downward direction $=Thrust/Area=E/8=4/8=0.5$
$\therefore$Pressure acting on water $=E/8=0.5$ (according to Pascal's Law)
(ii) $\therefore$ Pressure acting on piston $B=E/8=0.5$ (according to Pascal's Law)
(iii) Thrust acting on piston B in the upward direction $=Pressure\times AreaofB$

$=\frac{E\times 320}{8}=160$