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 with the bottom of the vessel. If r << R and the surface tension of water is T, the value of r just before bubbles detach is (density of water is ${\rho }_w$).

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

Answer 1

The correct option is D

$R^2\sqrt{\frac{2{\rho }_{w}g}{3T}}$

Force due to excess pressure = Upthrust
$\Rightarrow \frac{2T}{R}\left(\pi r^2\right)=\frac{4\pi }{3}{R}^3{\rho }_{w}g\therefore r=R^2\sqrt{\frac{2{\rho }_{w}g}{3T}}$