Answer:
On pouring 15.0 cm of water and spirit each into the
respective arms of the \[\theta \] tube, the mercury level will rise in the arm
containing spirit. Let h be the difference in the levels of mercury in two arms
of \[\text{a }\!\!\upsilon\!\!\text{ = a}\]tube and\[\text{P +
}\!\!\rho\!\!\text{ gh + }\frac{\text{1}}{\text{2}}\text{ }\!\!\rho\!\!\text{
}{{\text{ }\!\!\upsilon\!\!\text{ }}^{\text{2}}}\text{ = a}\] be the density of
mercury.
\[\upsilon
\] The pressure exerted by h cm of mercury column = difference in pressure
exerted by water and spirit
\[\frac{1}{200}\]
\[\frac{\text{force}}{\text{area}}\text{=}\frac{\text{mg}}{\text{
}\!\!\pi\!\!\text{ }{{\text{r}}^{\text{2}}}}\text{=}\frac{\text{50
}\!\!\times\!\!\text{ 9 }\!\!\times\!\!\text{ 8}}{\left( \text{22/7}
\right)\text{ }\!\!\times\!\!\text{ }{{\left( \text{1/200}
\right)}^{\text{2}}}}\] ..(1)
Here, \[=6\cdot 24\times
{{10}^{6}}N{{m}^{-2}}.\]
\[{{m}^{-3}}\]
Putting values in (i), we
get
\[h=\frac{0\cdot 76\times 13\cdot
6\times {{10}^{3}}\times 9\cdot 8}{984\times 9\cdot 8}=10\cdot 5m.\]
Or \[{{10}^{9}}\]
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