Properties of Matter 4 Question 6
8. 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
(2007, 3M)
(a) $\left|2 p_0 R h+\pi R^2 \rho g h-2 R T\right|$
(b) $\left|2 p_0 R h+R \rho g h^2-2 R T\right|$
(c) $\left|p_0 \pi R^2+R \rho g h^2-2 R T\right|$
(d) $\left|p_0 \pi R^2+R \rho g h^2+2 R T\right|$
Show Answer
Answer:
Correct Answer: 8. (b)
Solution:
- 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 $\left|2 p _0 R h+R \rho g h^{2}-2 R T\right|$
