GATE 2017 CE (CE2) – Question 55
An open U-tube of uniform square cross section 5 mm × 5 mm initially has mercury (specific gravity 13.6) standing 20 cm high in each vertical limb. When 5 cm³ of water is added to the right limb, the mercury height in the left limb, to two decimals, is ______ cm.
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Correct answer: 20.70 to 20.76
Explanation
Limb area is $0.5(0.5)=0.25$ cm². The added water column is $5/0.25=20$ cm. Equal limb areas mean mercury rises x on the left and falls x on the right. Hydrostatic balance gives $13.6(2x)=20$, hence $x=0.735294$ cm. New left height is $20+x=20.74$ cm.