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 $(p_A,p_E,p_C,p_D$ 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 $\rho gh$. Let radius of circle is $r$
$p_A=p_0+h\rho g$
$p_B=p_D=p_0+(h+r)\rho g$
$p_C=p_0+(h+2r)\rho g$
Then,
$p_C+p_A=\left[p_0+(h+2r)\rho g\right]-\left[p_0+h\rho g\right]$
$=p_0+h\rho g+2r\rho g+p_0+h\rho g$
$=2[p_0+(h+r)$
$\frac{p_C+p_A}{2}=p_0+(h+r)\rho g$
$\frac{p_C+p_A}{2}=p_B=p_D$
i.e., option (1), (2) and (4) gives correct statement but incorrect statement is (3)