Question

In a U-tube in which the cross-sectional area of the limb on the left is one-quarter, the limb on the right contains mercury (density $13.6g/c{m}^3$), and the level of mercury in the narrow limb is at a distance of $36cm$ 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. $1.2cm$
• B. $2.35cm$
• C. $0.56cm$
• D. $0.8cm$

Answer 1

The correct option is C $0.56cm$

Now it is given that the right limb cross-sectional area is 4 times that of the left limb.

So, if mercury in the right limb goes up by $x$, then the left limb will go down by $4x$.

Now equating the pressure at the interface AB.

We get, $(36+4x)\times 1\times g=5x\times 13.6\times g$

Or, $x=\frac{36}{64}$ or, $x=0.56$

hence Option C is correct