A $U$ tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10\,\, mm$ above the water level on the other side. Meanwhile the water rises by $65\,\, mm$ from its original level (see diagram). The density of the oil is ......... $kg/m^3$
NEET 2017, Diffcult
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Pressure at point $C$,
${p_C} = {p_a} + {\rho _{water}}g{h_{water'}}$
$where\,{h_{water}} = CE = \left( {65 + 65} \right)mm = 130\,mm$
$pressure\,at\,point\,B,{P_B} = {P_u} + {\rho _{oil}}g{h_{oil}}$
$where\,{h_{oil}} = AB = \left( {65 + 65 + 10} \right)\,mm = 140\,mm$
In liquid, Pressure is same at same liquid level,
${p_B} = {p_c} \Rightarrow {\rho _{oil}}g{h_{oil}} = {\rho _{water}}g\,{h_{water}}$
${\rho _{oil}} = \frac{{130 \times {{10}^3}}}{{140}} = \frac{{13}}{{14}} \times {10^3} = 928.57\,kg\,{m^{ - 3}}$
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