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

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(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.

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