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Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$, the surface tension of water is $T$ and the atmospheric pressure is $p_0$. Consider a vertical section $A B C D$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude.
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Verified Answer
The correct answer is:
$\left|2 p_0 R h+R \rho g h^2-2 R T\right|$
$\left|2 p_0 R h+R \rho g h^2-2 R T\right|$
Force from right hand side liquid on left hand side liquid.
(i) Due to surface tension force $=2 R T$ (towards right)
(ii) Due to liquid pressure force
$$
\begin{aligned}
& =\int_{x=0}^{x=h}\left(p_0+\rho g h\right)(2 R \cdot x) d x \\
& =\left(2 p_0 R h+R \rho g h^2\right) \text { (towards left) }
\end{aligned}
$$
$\therefore$ Net force is $\left|2 p_0 R h+R \rho g h^2-2 R T\right|$ Correct option is (b).
(i) Due to surface tension force $=2 R T$ (towards right)
(ii) Due to liquid pressure force
$$
\begin{aligned}
& =\int_{x=0}^{x=h}\left(p_0+\rho g h\right)(2 R \cdot x) d x \\
& =\left(2 p_0 R h+R \rho g h^2\right) \text { (towards left) }
\end{aligned}
$$
$\therefore$ Net force is $\left|2 p_0 R h+R \rho g h^2-2 R T\right|$ Correct option is (b).
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