1.

When liquid medicine rho is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop froms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is osperical becaus ethat requires a minimum increase in its surface energy. To datermine 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 become smaller than the wight of the drop, the drop gets detached from the droppr. A glass capillary tube is of the shape of a truncated cone with an apex angle alpha so that its two ends have cross sections of different raddi. When dipped in water verically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is rho, and its contact angle with glass is theta, the value of h will be (g is the acceleration due to gravity)

Answer»

`(2S)/(brhog)cos(theta-alpha)`
`(2S)/(brhog)cos(theta+alpha)`
`(2S)/(brhog)cos(theta-alpha//2)`
`(2S)/(brhog)cos(theta+alpha//2)`

Solution :Using geometery : `(B)/(R_(e)) = cos(theta + (alpha)/(2))`
Using PRESSURE method : `P_(0) - (2S)/(R_(c)) + hrhog = P_(0)`
`RARR H = (2S)/(R_(e)rhog) = (2S)/(brhog)cos(theta + alpha//2)`


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