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Question

(C) Points at the same horizontal level in a continuous static liquid have the same pressure. Points at different depths have a pressure difference gi

Vedclass · Accepted Answer

$p_D = p_B = \frac{p_C - p_A}{2}$

Vedclass · Answer

(C) Points at the same horizontal level in a continuous static liquid have the same pressure. Points at different depths have a pressure difference given by $\Delta p = \rho g \Delta h$.Let the radius of the circle be $r$ and the depth of point $A$ from the free surface be $h$. Let $p_0$ be the atmospheric pressure.The absolute pressures at the points are:$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$Now,let us evaluate the expressions in the options:$1$. $p_D = p_B$ is correct as they are at the same horizontal level.$2$. Since $h $3$. Calculating the average of $p_A$ and $p_C$:$\frac{p_C + p_A}{2} = \frac{(p_0 + h \rho g + 2r \rho g) + (p_0 + h \rho g)}{2} = \frac{2p_0 + 2h \rho g + 2r \rho g}{2} = p_0 + (h + r) \rho g = p_B = p_D$.Thus,the statement $p_D = p_B = \frac{p_C + p_A}{2}$ is correct,and the statement $p_D = p_B = \frac{p_C - p_A}{2}$ is incorrect.Therefore,option $(c)$ is the incorrect statement.

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