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 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 \(\rho_{w}\))

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) \(R^{2} \sqrt{\frac{2 \rho_{w} g}{3 T}}\)

Detailed explanation

When the bubble gets detached,

Buoyant force = force due to surface tension

\(\int T \times d l \sin \theta=\frac{4}{3} \pi R^{3} \rho_{w} g\)

\(\Rightarrow T \times 2 \pi r \times \frac{r}{R}=\frac{4}{3} \pi R^{3} \rho_{w} g\)

\(\Rightarrow r^{2}=\frac{2 R^{4} \rho_{w g} g}{3}\)

\(\Rightarrow r=R^{2} \sqrt{\frac{2 \rho_{w D g}}{3 T}}\)

Same subject

From JEE Mains

List - I	List - II
(A) Electric field inside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(I) \(\sigma / \epsilon_0\)
(B) Electric field at distance \(r >0\) from a uniformly charged infinite plane sheet with surface charge density \(\sigma\).	(II) \(\sigma / 2 \epsilon_0\)
(C) Electric field outside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(III) \(0\)
(D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density \(\sigma\).	(IV) \(\frac{\sigma R^2}{\epsilon_0 r^2}\)