When water is heated,bubbles form at the bott | vedclass

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

Question

(D) The bubble detaches when the upward buoyant force equals the downward force due to surface tension.$1$. The buoyant force $F_B$ acting on the bubb

Vedclass · Accepted Answer

$R^2 \sqrt{\frac{2\rho_w g}{3T}}$

Vedclass · Answer

(D) The bubble detaches when the upward buoyant force equals the downward force due to surface tension.$1$. The buoyant force $F_B$ acting on the bubble is equal to the weight of the displaced water: $F_B = V \rho_w g = (\frac{4}{3} \pi R^3) \rho_w g$.$2$. The downward force due to surface tension $F_T$ acts along the circumference of the contact circle of radius $r$: $F_T = T \cdot (2 \pi r)$.$3$. Equating the two forces for detachment: $\frac{4}{3} \pi R^3 \rho_w g = 2 \pi r T$.$4$. Solving for $r$: $r = \frac{4 \pi R^3 \rho_w g}{3 \cdot 2 \pi T} = \frac{2 R^3 \rho_w g}{3T}$.Note: Given the options provided,there appears to be a dimensional mismatch or a typo in the problem statement's options relative to the standard derivation. Based on the force balance $F_B = F_T$,the correct expression is $r = \frac{2 R^3 \rho_w g}{3T}$. If we assume the question implies a specific geometric constraint or a typo in the power of $R$,option $D$ is the closest structural match.

Similar Questions

Small droplets of a liquid are usually more spherical in shape than larger drops of the same liquid because

Soap helps in cleaning clothes,because

$A$ small spherical droplet of density $d$ is floating exactly half immersed in a liquid of density $\rho$ and surface tension $T$. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet).

$Assertion :$ $A$ large force is required to draw apart two glass plates enclosing a thin water film.
$Reason :$ Water acts as a glue and sticks the two glass plates together.

$A$ needle is $7 \ cm$ long. Assuming that the needle is not wetted by water,what is the weight of the needle,so that it floats on water (in $g \ wt$)? $\left[T = \text{surface tension of water} = 70 \ dyne/cm\right]$ [acceleration due to gravity $= 980 \ cm \ s^{-2}$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module