Question 353: Properties of Matter

Question

Three liquids of densities $ho $
1
, $ho $
2
and $ho $
3
(with $ho $
1
> $ho $
2
> $ho $
3
), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $	heta $
1
, $	heta $
2
and $	heta $
3
obey

Accepted Answer

Capillary rise, $h = {{2T\cos heta } \over {r ho g}}$ For given value of T and $r,h \propto {{\cos heta } \over ho }$ Also, ${h_1} = {h_2} = {h_3}$ or ${{\cos { heta _1}} \over {{ ho _1}}} = {{\cos { heta _2}} \over {{ ho _2}}} = {{\cos { heta _3}} \over {{ ho _3}}}$ Since, ${ ho _1} > { ho _2} > { ho _3}$, so ${\cos { heta _1} > \cos { heta _2} > \cos { heta _3}}$ For $0 \le heta < {\pi \over 2},{ heta _1} < { heta _2} < { heta _3}$ Hence, $0 \le { heta _1} < { heta _2} < { heta _3} < {\pi \over 2}$

Answer

${\pi  \over 2} > {	heta _1} > {	heta _2} > {	heta _3} \ge 0$

Answer

0 $ \le $ $	heta $
1
< $	heta $
2
< $	heta $
3
< ${\pi  \over 2}$

Answer

${\pi  \over 2} < {	heta _1} < {	heta _2} < {	heta _3} < \pi $

Answer

$\pi  > {	heta _1} > {	heta _2} > {	heta _3} > {\pi  \over 2}$

Properties of Matter

Three liquids of densities \rho 1 , \rho 2 and \rho 3 (with \rho 1 > \rho 2 > \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

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