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Three liquids of densities rho1,rho2 and...

Three liquids of densities `rho_1`,`rho_2` and `rho_3` (with `rho_1gtrho_2gtrho_2)` 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 lt theta_1 lt theta_2 lt theta_3 ltpi`

B

`pi gt theta_1 gt theta_2 gt theta_3 gtpi/2`

C

`pi/2 gt theta_1 gt theta_2 gt theta_3 ge0`

D

`0 le theta_1lt theta_3lt theta_3 ltpi/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`h = (2T cos theta)/(rho gr)`
as r,h,T are same
`implies (cos theta)/rho` = constant `implies (cos theta_1)/rho_1 =(cos theta_2)/rho_2 =(cos theta_3)/rho_3`
as `rho_1 gt rho_2 gt rho_3`
`implies cos theta_1 gt cos theta_2 gt cos theta_3 implies theta_1 lt theta_2 lt theta_3`
As water rises, `theta` must be acute
So, `0 le theta_1 lt theta_2 lt theta_3 lt pi//2`
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