A cappilary of diameter d mm is dipped in water such that the water rises to a height of 30 mm. If the radius of the capillary is made `((2)/(3))` of its previous value, then compute the height up to which water will rise in the new capillary ?

Explanation

We know the height of the capillary rise `h = (2T cos theta)/(r dg)`
where T = surface tension, r = radius , d = density , g = acceleration due to gavity
Now, `h_1r_1 = h_2r_2implies (h_2)/(h_1) = (r_1)/(r_2)`
Here , `r_2 = 2/3 r_1 and h_1 = 30 mm`
`h_2 = (r_1)/((2/3)r_1) xx 30 = 3/2 xx 30`
`h_2 = 45 mm`.