On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be sphere 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 ρw)

Engineering

Physics

Surface Tension and Surface Energy

Question

On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be sphere 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 ρ_w)

$R^{2} \sqrt{\frac{2 ρ_{w} g}{3 T}}$

$R^{2} \sqrt{\frac{ρ_{w} g}{T}}$

$R^{2} \sqrt{\frac{3 ρ_{w} g}{T}}$

$R^{2} \sqrt{\frac{ρ_{w} g}{6 T}}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$\frac{4}{3} {πR}^{3} - ρ_{w} q$

= T × 2πr sin $θ$

$= T \times \frac{2 {πr}^{2}}{R}$

$Ans r = R^{2} \sqrt{\frac{2}{3} \frac{ρ_{w} g}{T}}$