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

Let diameter of capillary tube = dmm
Let radius of capillary tube `r_(1)=rmm`
Capillary rise `h_(1)=30mm`
Let the radius of another capillary tube `r_(2)=(2)/(3)r`
Let capillary rise of another capillary tube be `h_(2)`
We know that
`T=(hrrhog)/(2)`
`thereforehprop(1)/(r)`
`(h_1)/(h_2)=(r_2)/(r_1)`
`(3)/(h_2)=((2)/(3)r)/(r)`
`(3)/(h_2)=(2)/(3)`
`thereforeh_(2)=(3xx30)/(2)=45mm`
`{:("Capillary rise in the"),("new capillary tube"):}}=45mm`