Question

The area of cross-section of one limb of an $U-tube$ is twice that of other. Both the limbs contain mercury at the same level. Water is poured in the wider tube so that mercury level in it goes down by 1 cm. The height of water column is (density of water $={10}^{3}kg{m}^{-3},$ density of mercury $=13.6\times {10}^3$ $kg{m}^{-3}$ )

• A. 13.6m
• B. 40.8m
• C. 27.2m
• D. 54.4m
• E. 6.8m

Answer 1

Answer: (B)

The depression of level in the left limb is 1 cm, so the rise of level of mercury in right limb be 2 cm, because the area of cross-section of left limb is twice as that of right limb.
Now, equating pressure at interface of mercury and water (at AB)
$(x+1)\times {10}^3\times g=(1+2)\times 13.6\times {10}^{3}g$
or height of water column $x+1=40.8m$