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When liquid medicine of density $$\rho$$ is to be put in theeye, it is done with the help of a dropper. As the bulb onthe topof the dropperis pressed, a drop forms at the opening of the dropper. We wishto estimate the size of the drop. Wefirst assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

Question 50

If the radius of the opening of the dropperis r, the vertical force due to the surface tension on the drop of radius R (assuming $$r \ll R$$) is

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