A liquid is placed in a cylindrical glass container of radius R0. In gravity free space, free surface of liquid has spherical shape of all radius of curvature R1. Now same liquid is placed in a large spherical glass container of radius R2 in uniform gravity. If surface of liquid in spherical container is found to be flat, then find the height of liquid surface in spherical container from centre of container.

Engineering

Physics

Liquid Pressure

Surface Tension and Surface Energy

Capillary and Pressure Difference due to Surface Tension

Question

A liquid is placed in a cylindrical glass container of radius R₀. In gravity free space, free surface of liquid has spherical shape of all radius of curvature R₁. Now same liquid is placed in a large spherical glass container of radius R₂ in uniform gravity. If surface of liquid in spherical container is found to be flat, then find the height of liquid surface in spherical container from centre of container.

$\sqrt{\frac{R_{1} R_{2}}{R_{0}}}$

$R_{0} \frac{R_{1}}{R_{2}}$

$\frac{R_{1} R_{2}}{R_{0}}$

$R_{0} \frac{R_{2}}{R_{1}}$

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Contact angle (θ) will remain same

$figure (1) \sin (90 - θ) = \frac{R_{0}}{R_{1}}; cosθ \frac{R_{0}}{R_{1}} . ........ (i)$

$Fig (2) cosθ = \frac{h}{R_{2}} . . . . . . . . . . . . . . . . . . . . (ii); \frac{h}{R_{2}} = \frac{R_{0}}{R_{1}} \Rightarrow h = \frac{R_{0} R_{2}}{R_{1}}$