Q: Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ , the surface tension of water is T and the atmosphere pressure is p_{0}. Consider a vertical section ABCD of the water column through a diameter of the breaker. The force on water on one side of this section by water on the other side of this section has magnitude

(a) $\large 2 p_0 R h + \pi R^2 \rho g h – 2 R T$

(b) $\large 2 p_0 R h + R \rho g h^2 – 2 R T$

(c) $\large p_0 R^2 + R \rho g h^2 – 2 R T$

(d) $\large p_0 R^2 + R \rho g h^2 + 2 R T$

Ans: (b)

Sol: 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

$\large = \int_{x=0}^{x=h}(p_0 + \rho g h)(2R . x)dx $

$\large = (2 p_0 R h + R \rho g h^2)$ (towards left)

Net Force $\large = (2 p_0 R h + R \rho g h^2 – 2 R T)$