Question

A U-tube is partially filled with water. Oil, which does not mix with water, is next poured into one side until water rises by $25cm$. On the other side, if the specific gravity of oil be $0.8$, the oil level will stand higher than the water level by:

• A. $6.25cm$
• B. $12.50cm$
• C. $31.25cm$
• D. $62.50cm$

Answer 1

Answer: (A)

$6.25cm$

Let's assume that the oil is y cm above the water level. If ${\rho }_o$ be the density of oil and ${\rho }_w$ be the density of water.

By using Pascal's law:

(Pressure at the same level of both the arms of the U-tube will be same)

$y$${\rho }_o$$g$ $+$$25$${\rho }_w$$g$$=$ $50$${\rho }_w$$g$

$25$ ${\rho }_w$$g$$=$ y ${\rho }_o$$g$

$y=31.25cm$

Hence the oil will stand $31.25-25=6.25cm$ above water level.