A capillary tube of radius 'r' is immersed in water and water rises to a height of 'h'. Mass of water in the capillary tube is `5 xx 10^ -3 kg`. The same capillary tube is now immersed in a liquid whose surface tension is sqrt2 times the surface tension of water. The angle of contact between the capillarv tube and this liauid is `45^@`. The mass of liquid which rises into the capillary tube now is (in kg)

Options

A. `5xx 10^-3`
B. `2.5xx 10^-3`
C. `5sqrt2 xx10^-3`
D. `3.5xx10^-3`

Answer

A

Explanation

Rise in water level in a capillary tube,
`h=(2Tcostheta)/(rdg)`
`=(2T)/(rdg)[because theta=0"initially"]`
`h_(1)=(2xxsqrt(2)xx(1/sqrt(2)))/(rdg)`
`[because "Given", at h=h_(1), T=sqrt(2) T and theta=45^@]`
`(2T0)/(rdg)`
`therefore h_(1)=h`
`therefore "Mass of the liquid that rises in capillary is" 5xx10^(-3) kg`.