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A liquid rises to a height of 1.8 cm in...

A liquid rises to a height of 1.8 cm in a glass capillary A another glass capillary B having diameter 90% of capillary A is immersed in the same liquid the rise of liquid in capillary B is

A

`1.4 cm`

B

1.8 cm

C

`2.0 cm`

D

2.2 cm

Text Solution

Verified by Experts

The correct Answer is:
C
Height of liquid in a capillary tube `h = (2S cos theta)/(r rho g)`
where, S = surface tension
`rho` = density of the liquid
r = radius of the capillary tube
For capillary A, `h_(A) = (2S cos theta)/(r_(A) rho g)` ...(i)
For capillary B, `h_(B) = (2S cos theta)/(r_(B) rho g)` ...(ii)
from Eqs. (i) and (ii),
`h_(A) r_(A) = h_(B)r_(B)`
`rArr (1.8 cm)(r_(A)) = (h_(B)) ((90)/(100) xx r_(A))`
or `(1.8 cm) = h_(B) xx (9)/(10)`
or `h_(B) = (10)/(8) xx 1.8 cm = 2 cm`
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