Question 201: Properties of Matter

Question

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius $r$ with the bottom $R$ and making a circular contact of radius $r$ with the bottom of the vessel. If $r <  < R$ and the surface tension of water is $T,$ value of $r$ just before bubbles detach is: (density of water is ${\rho _w}$)
![](https://imagex.cdn.examgoal.net/N1zIkQaXtjHRkHohx/eg9tvXTZ3VBbAw2akKXcbp4ktNtAr/9kPdF4iFlDnaf4fbJEoO4M/image.png)

Accepted Answer

When the bubble gets detached, Buoyant force $=$ force due to surface tension
Force due to excess pressure $=$ upthrust
Access pressure in air bubble $ = {{2T} \over R}$
${{2T} \over R}\left( {\pi {r^2}} \right) = {{4\pi {R^3}} \over {3T}}{\rho _w}g$
$ \Rightarrow {r^2} = {{2{R^4}{\rho _w}g} \over {3T}}$
$ \Rightarrow r = {R^2}\sqrt {{{2{\rho _w}g} \over {3T}}} $
![](https://imagex.cdn.examgoal.net/4opxg7CIM1cnXllBE/PScFKI5eBj7YljehjKHkERwF9abNK/rSO7r9I8VzLo9cmM42UBcV/image.svg)

Answer

${R^2}\sqrt {{{{\rho _w}g} \over {3T}}} $

Answer

${R^2}\sqrt {{{{\rho _w}g} \over {6T}}} $

Answer

${R^2}\sqrt {{{{\rho _w}g} \over {T}}} $

Answer

${R^2}\sqrt {{{{2\rho _w}g} \over {3T}}} $

Properties of Matter

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