Question

On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius $R$ 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 detatch is (density of water is ${\rho }_w$ )

• A. $R^2\sqrt{\frac{2{\rho }_{w}g}{3T}}$
• B. $R^2\sqrt{\frac{{\rho }_{w}g}{6T}}$
• C. $R^2\sqrt{\frac{{\rho }_{w}g}{T}}$
• D. $R^2\sqrt{\frac{3{\rho }_{w}g}{T}}$

Answer 1

Answer: (A)

When the bubble gets detached,
Buoyant force = force due to surface tension

$\int T\times dl\sin \theta =\frac{4}{3}\pi R^3{\rho }_{w}g$
$\Rightarrow T\times 2\pi r\times \frac{r}{R}=\frac{4}{3}\pi R^3{\rho }_{w}g$
$\Rightarrow r^2=\frac{2R^4{\rho }_{w}g}{3}$
$\Rightarrow r=R^2\sqrt{\frac{2{\rho }_{wD}g}{3T}}$