A drop of liquid of density rho is floating h | vedclass

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

Question

(A) For the drop to be in equilibrium,the upward forces (buoyant force and surface tension force) must balance the downward force (weight of the drop)

Vedclass · Accepted Answer

$\frac{15}{\sqrt{2\rho - \sigma}}$

Vedclass · Answer

(A) For the drop to be in equilibrium,the upward forces (buoyant force and surface tension force) must balance the downward force (weight of the drop).Let $R$ be the radius of the drop. The volume of the drop is $V = \frac{4}{3}\pi R^3$.Buoyant force $F_b = 	ext{Volume immersed} 	imes \sigma 	imes g = \frac{V}{2} \sigma g = \frac{2}{3}\pi R^3 \sigma g$.Surface tension force $F_T = T 	imes (2\pi R) = 2\pi RT$.Weight of the drop $W = mg = V ho g = \frac{4}{3}\pi R^3 ho g$.Equating forces: $F_b + F_T = W$$\frac{2}{3}\pi R^3 \sigma g + 2\pi RT = \frac{4}{3}\pi R^3 ho g$$2\pi RT = \frac{4}{3}\pi R^3 ho g - \frac{2}{3}\pi R^3 \sigma g = \frac{2}{3}\pi R^3 g (2ho - \sigma)$$T = \frac{R^2 g (2ho - \sigma)}{3} \Rightarrow R^2 = \frac{3T}{g(2ho - \sigma)}$Given $T = 7.5 	imes 10^{-4} \, N/cm = 7.5 	imes 10^{-2} \, N/m$ and $g = 10 \, m/s^2$:$R = \sqrt{\frac{3 	imes 7.5 	imes 10^{-2}}{10(2ho - \sigma)}} = \sqrt{\frac{22.5 	imes 10^{-2}}{10(2ho - \sigma)}} = \sqrt{\frac{2.25 	imes 10^{-2}}{2ho - \sigma}} = \frac{0.15}{\sqrt{2ho - \sigma}} \, m$Converting to $cm$ $(1 \, m = 100 \, cm)$:$R = \frac{0.15 	imes 100}{\sqrt{2ho - \sigma}} \, cm = \frac{15}{\sqrt{2ho - \sigma}} \, cm$.

$A$ drop of liquid of density $\rho$ is floating half-immersed in a liquid of density $\sigma$ and surface tension $T = 7.5 \times 10^{-4} \, N \, cm^{-1}$. The radius of the drop in $cm$ will be: (Take: $g = 10 \, m/s^2$)

Similar Questions

Assertion $(A)$: At critical temperature,the surface tension of liquids becomes zero.
Reason $(R)$: At critical temperature,the intermolecular forces for liquids and gases become equal.

On what factors does the value of surface tension depend? Explain.

Explain why is hot soup more tasty than the colder one?

$A$ $10\, cm$ long wire is placed horizontally on the surface of water and is gently pulled up with a force of $2 \times 10^{-2}\, N$ to keep the wire in equilibrium. The surface tension,in $N/m$,of water is:

The surface tension of a liquid at its boiling point

Vedclass Test Series

Exam Paper Generator

Online Exam Module