A barometer contains two uniform capillaries of radii `1.4xx10^(-3)m` and `7.2xx10^(-4)m`. If the height of liquid in narrow tube is `0.2m` more than that in wide tube, calculate the true pressure difference. Density of liquid `=10^(3)kg//m^(3)`, surface tension `=72xx10^(-3)N//m` and `g=9.8ms^(-12)`.

Answer

A, B

Explanation

Let the pressures in the wide and narrow capollaries of radii `r_(1)` and `r_(2)` respectively be `p_(1)` and `p_(2)`. Then pressure just below the meniscus in the wide and narrow tubes reapectively are
`(p_(1)-(2T)/(r_(1)))` and `(p_(2)-(2T)/(r_(2)))`
[excess pressure`=(2T)/(r)]`

Different in these pressures
`(p_(1)-(2T)/(r_(1))) - (p_(2)-(2T)/(r_(2)))=hrhog`
`:.` True pressure difference `=p_(1)-p_(2)`
`=hrhog+2T((1)/(r_(1))-(1)/(r_(2)))`
`=0.2xx10^(3)xx9.8+2xx72xx10^(-3)`
`[(1)/(1.44xx10^(-3))-(1)/(7.2xx10^(-4))]`
`=1.86xx10^(3)=1860N//m^(2)`.