Question

Figure shows a container filled with a liquid of density $\rho$. Four points $A, B, C$ and $D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on vertical line and points $B$ and $D$ lie on horizontal line. The incorrect statement is $\left(p_{A}, p_{E}, p_{C}, p_{D}\right.$ are absolute pressure at the respective points)

• A. $p_{D}=p_{B}$
• B. $p_{A} < p_{B}=p_{D} < p_{C}$
• C. $p_{D}=p_{B}=\frac{p_{C}-p_{A}}{2}$
• D. $p_{D}=p_{B}=\frac{p_{C}+p_{A}}{2}$

Answer 1

Answer: (C)

Points at same height have same pressure, points with height difference say ' $h$ ' will have difference of $\rho g h$. Let radius of circle is $r$
$p_{A}=p_{0}+h \rho g$
$p_{B}=p_{D}=p_{0}+(h +r) \rho g$
$p_{C}=p_{0}+(h+2 r) \rho g$
Then,
$p_{C}+p_{A} =\left[p_{0}+(h+2 r) \rho g\right]-\left[p_{0}+h \rho g\right]$
$=p_{0}+h \rho g+2 r \rho g +p_{0}+h \rho g$
$=2\left[p_{0}+(h+ r)\right.$
$\frac{p_{C}+p_{A}}{2} =p_{0}+(h +r) \rho g$
$\frac{p_{C}+p_{A}}{2} =p_{B}=p_{D}$
i.e., option (1), (2) and (4) gives correct statement but incorrect statement is (3)