In a capillary tube having area of cross - section A, water rises to a height h. If cross-sectional area is reduced to `(A)/(9)`, the rise of water in the capillary tube is

Options

A. 4h
B. 3h
C. 2h
D. h

Answer

B

Explanation

For a capillary tube,
rh=constant where, r=radius of capillary tube and h=height of rised water in capilliary tube According to the question,
`r_(1)h_(1)=r_(2)h_(2)`
`rArr" "(r_(1))/(r_(2))=(h_(2))/(h_(1))` . . .. (i)
In the first condition,
`A_(1)=pir_(1)^(2)` . . .(ii)
In the second condition,
`A_(2)=pir_(2)^(2)`
or `(A)/(9)=pir_(2)^(2)" "[as,A_(2)=(A)/(9)]` . . .(iii)
On dividing Eq.(ii) by Eq. (iii), we get
`9=(r_(1)^(2))/(r_(2)^(2))" or"(r_(1))/(r_(2))=sqrt(9)rArr(r_(1))/(r_(2))=3`
From Eq. (i), we get
`(h_(2))/(h_(1))=3rArrh_(2)=3h_(1)`
`h_(2)=3h`