JEE Main 2014 · 6 Apr · Shift 1 · Physics Q10

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PhysicsSingle correct+4 / -1Question 10 of 90

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 $r\ll R$ , and the surface tension of water is $T$ , value of $r$ just before bubbles detatch is :

(density of water is $\rho_w$ )

A vessel of water with a spherical bubble of radius R resting on the bottom, touching it over a small circle of diameter 2r.

R^2\sqrt{\dfrac{\rho_wg}{3T}}

R^2\sqrt{\dfrac{\rho_wg}{6T}}

R^2\sqrt{\dfrac{\rho_wg}{T}}

R^2\sqrt{\dfrac{3\rho_wg}{T}}

Answer and worked solution

Official answer: A

At detachment, buoyancy balances the vertical pull of surface tension round the contact circle. At the contact edge the surface makes angle $\theta$ with the horizontal, where $\sin\theta\approx\frac rR$ . So
$T\cdot2\pi r\cdot\frac rR=\frac43\pi R^3\rho_wg\implies r^2=\frac{2\rho_wgR^4}{3T},$
i.e. $r=R^2\sqrt{\dfrac{2\rho_wg}{3T}}$ .

This exact form is not among the options. The official key gives (1), $R^2\sqrt{\dfrac{\rho_wg}{3T}}$ , which has the same dependence on $R$ , $\rho_w$ , $g$ and $T$ and differs only by the factor $\sqrt2$ .

Topics:Surface tension Buoyancy and Archimedes' principle

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JEE Main 2014 · 6 Apr · Shift 1, Physics question 10