Question

A U - Tube in which the cross sectional area of the limb on the left is one quarter of the limb on the right (which contains mercury) (density $=13.6g/c{m}^3$). The level of mercury in the narrow limb is at distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb, if the left limb is filled to the top with water?

• A. 12 cm
• B. 2.35 cm
• C. 0.56 cm
• D. 0.8 cm

Answer 1

The correct option is C 0.56 cm

If the rise of level in the right limb be $x$ cm, the fall of level of mercury in left limb will be 4$x$ cm because area is one quarter than the right limb.
So, level of water in lift limb is $=$
(36 + 4$x$) cm
Now, equating pressure at interfaces of mercury and water $(36+4x)\times 1\times g=5\times 13.6\times g$
$x$ = 0.56 cm