Water is filled up to a height h in a beaker | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Consider a vertical rectangular strip of height $dx$ at a depth $x$ from the free surface of the water. The width of this strip is the diameter of

Vedclass · Accepted Answer

$\left|2 P_0 Rh+R \rho gh^2-2 RT\right|$

Vedclass · Answer

(B) Consider a vertical rectangular strip of height $dx$ at a depth $x$ from the free surface of the water. The width of this strip is the diameter of the beaker,which is $2R$.The pressure at depth $x$ is $P(x) = P_0 + \rho g x$.The force exerted by the pressure on this strip is $dF_p = P(x) \cdot (2R) dx = (P_0 + \rho g x) 2R dx$.Integrating this from $x = 0$ to $x = h$,the total force due to pressure is $F_p = \int_0^h (P_0 + \rho g x) 2R dx = 2R [P_0 x + \frac{1}{2} \rho g x^2]_0^h = 2 P_0 R h + R \rho g h^2$.Additionally,there is a force due to surface tension acting along the top edge of the section. The length of the section at the surface is $2R$,so the force due to surface tension is $F_T = T \cdot (2R) = 2RT$.Since the surface tension force acts in the opposite direction to the pressure force,the net magnitude of the force is $F = |F_p - F_T| = |2 P_0 R h + R \rho g h^2 - 2 RT|$.

Similar Questions

How does the surface tension of a liquid change with temperature?

Define surface tension with its formula in the context of intermolecular forces.

Write two units of surface tension and give the dimensional formula of surface tension.

Work of $3.0 \times 10^{-4} \, J$ is required to be done in increasing the size of a soap film from $10 \, cm \times 6 \, cm$ to $10 \, cm \times 11 \, cm$. The surface tension of the film is

$A$ soap film is formed on a circular frame. $A$ loop of thread is lying on the film. If the film inside the loop is broken,then the tension in the thread will be: ($R =$ radius of the loop,$T =$ surface tension of the liquid)

Vedclass Test Series

Exam Paper Generator

Online Exam Module