Question

A $U-$tube is partially filled with water and oil which does not mix with water is next poured into one side until water rises by $25cm$ on the other side. If the density of oil is $0.8$, the oil level will stand higher than the water level by:

• A. $6.25cm$
• B. $12.50cm$
• C. $31.75cm$
• D. $62.50cm$

Answer 1

The correct option is B $12.50cm$

At Level $A$

On $I$ tube

$P_{A_I}={\int }_{w}g{h}_w+{\int }_{o}g{h}_o$ $h_w=0,h_o=h$

$={\int }_o=0.8{\int }_{w}gh$

On tube $II$ tube

$P_{A_{II}}={\int }_{w}g{h}_w+{\int }_{o}g{h}_o$ $h_w=50,h_o=0$

$={\int }_{w}g\left(50\right)$

$P_{A_2}=P_{A_{II}}$

$0.8{\int }_{w}gh={\int }_{w}g\left(50\right)$

$h=\frac{50}{0.8}=\frac{500}{8}=62.5$

Difference between oil and water level

$=h-50$

$=62.5-50$

$=12.5$