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Three liquids of densities rho(1), rho(2...

Three liquids of densities `rho_(1), rho_(2) " and " rho_(3)` (with `rho_(1) gt rho_(2) gt rho_(3))`, having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact `theta_(1), theta_(2) " and " theta_(3)` obey

A

`(pi)/(2) gt theta_(1) gt theta_(2) gt theta_(3) ge 0`

B

`0 le theta_(1) lt theta_(2) lt theta_(3) lt (pi)/(2)`

C

`(pi)/(2) lt theta_(1) lt theta_(2) lt theta_(3) lt pi`

D

`pi gt theta_(1) gt theta_(2) gt theta_(3) gt (pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
b
According to ascent formula for capillary tube.
`H = (2T cos theta)/(rho gr)`
`:. (cos theta_(1))/(rho_(1)) = (cos theta_(2))/(rho_(2)) = (cos theta_(3))/(rho_(3))`
Thus, `cos theta prop rho`
`:. Rho_(1) gt rho_(2) gt rho_(3)`
`:. cos theta_(1) gt cos theta_(2) gt cos theta_(3)`
`0 le theta_(1) lt theta_(2) lt theta_(3) lt (pi)/(2)`
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