Question

A tube with both ends open floats vertically in water. Oil with a density $800\, kg / m ^{3}$ is poured into the tube. The tube is filled with oil up to the top end while in equilibrium. The portion out of the water is of length $10\, cm$. The length of the tube is:

• A. 50 cm
• B. 60 cm
• C. 90 cm
• D. 100 cm

Answer 1

Answer: (D)

After oil is filled up, pressure at the depth of lower end should equate if measured from inside and outside the tube. Suppose depth of oil is $x cm$ then:

$1000 \cdot g \cdot[(l-10) cm ]=800\, g \cdot(x cm )+1000\, g[(l-x) cm ]$
$\Rightarrow x=50\, cm$
Now, pressure difference due to $x cm$ depth of oil is equal to
pressure difference due to $(l-x-10) cm$ of water.
$\Rightarrow 800 \cdot g \cdot x=1000\, g (l-60)$
$\Rightarrow l=100\, cm$