Question

Two cylindrical tanks of radii $r$ and $2r$ with their bases at the same level contain a liquid of density $p$ to heights $H$ and $3H$, respectively as shown in figure, The tanks are linked through a pipe of very small cross-sectional area $A$. Due to pressure difference liquid starts flowing from narrower vessel to broader vessel to equalize the pressure.
Based on above information, answer the following questions:
The final common level of liquid in both vessel is

• A. $2H$
• B. $\frac{7H}{5}$
• C. $\frac{3H}{2}$
• D. $\frac{5H}{2}$

Answer 1

The correct option is B $\frac{7H}{5}$

Let P be the final level of the fluid,

The total volume should be same.

Let the amount of fluid contained in the U tube be

$V_{initial}=C+\pi r^2\times 3H+4\pi r^2\times H$

$=C+7\pi r^{2}H$

$V_{final}=c+\pi r^2\times p+4\pi r^{2}p$

$=C+5\times \pi r^{2}p$

$C+\pi r^{2}H=C+5\pi r^{2}p$

$p=\frac{7}{5}H$