Question

A $U-$tube is partically field with warter. Oil which does not mix with water is next poured into one side, unit water rises by $25cm$ on the other side. If the density of the oil is $0.8g/cc$, then oil level will stand higher then the water level by

• A. $6.25cm$
• B. $12.50cm$
• C. $18.75cm$
• D. $25.00$

Answer 1

The correct option is A $6.25cm$

Given,

A U-tube is partially field with water

Given,

Oil does not mix with water is next poured into one side,

Unit water rises by $=25cm$

Density of the oil$=0.8g/cc$

The oil level will stand higher than the water level.

Solution

It is important to recall that as the water and oil levelsare stationary the pressure exerts by both columns in the tube would be equal

So

$P\left(water\right)=P\left(oil\right)or,{\rho }_{\omega }{h}_{\omega }g={\rho }_{oil}g{h}_{oil}{\rho }_{\omega }g\times 25={\rho }_{oil}g{h}_{oil}{h}_{oil}=\frac{{\rho }_{\omega }\times 25}{{\rho }_{oil}}=\frac{25}{0.8}=31.25cm$

Difference in the height will be

$=(31.25-25)cm=6.25cm$