State and prove the theorem of 'parallel axis'. Calculate the density of paraffin oil, if glass capillary of diameter 0.25 mm dipped in paraffin oil of surface tension 0.0245 N/m rises to a height of 4 cm. (Angle of contact of paraffin with glass `=28^(@)` and acceleration due to gravity `=9.8" m"//"s"^(2)`.)

Explanation

Given : Diameter of capillary
`=0.25" mm",`
`r=.125xx10^(-3)" m"`
Surface Tension (T) `=0.0245" N"/"m"`
Height, `h=4" cm"=0.04" m"`
`g=9.8" m"//"s"^(2)`
`theta=28^(@)`
Let,
density of paraffin oil = `rho`
`because" "T=(rhrhog)/(2 cos theta)`
`implies" "0.0245=(0.125xx10^(-3)xx4xx10^(-2)xxrhoxx9.8)/(2xxcos 28^(@))`
`implies" "rho=882.9" kg"//"m"^(3)`