Q. A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density $= 1.3\ g/cm^{3}$) column of length $10\ cm$ is introduced into one of its arms. Oil of density $0.8\ gm/cm^{3}$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column. Density of mercury $= 13.6\ g/cm^{3}$
A) $10.4\ cm$
B) $8.2\ cm$
C) $7.2\ cm$
D) $9.6\ cm$
Explanation
(d) At the condition of equilibrium
Pressure at point $A =$ Pressure at point $B$
$P_{A} = P_{B} \Rightarrow 10 \times 1.3 \times g = h \times 0.8 \times g + (10 - h) \times 13.6 \times g$
By solving we get $h = 9.6\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.