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Question

Physics Question on mechanical properties of fluid

An open U-tube contains mercury. When 11.2cm11.2 \,cm of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm form its initial level?

A

0.56 cm

B

1.35 cm

C

0.41 cm

D

2.32 cm

Answer

0.41 cm

Explanation

Solution

Key Idea : At the same level in the two limbs of a U-tube, pressure is same.
On pouring water on left side, mercury rises xcmx cm (say) from its previous level in the right limb of UU-tube creating a difference of levels of mercury by 2xcm2 x\, cm. Equating pressures at AA and BB, we get


PA=PBP_{A}=P_{B}
11.2×102×ρwater ×g=2x×ρmercury ×g\therefore 11.2 \times 10^{-2} \times \rho_{\text {water }} \times g=2 x \times \rho_{\text {mercury }} \times g
11.2×102×1000kg/m3\Rightarrow 11.2 \times 10^{-2} \times 1000\, kg / m ^{3}
=2x×13600×kg/m3=2 x \times 13600 \times\, kg / m ^{3}
x=11.2×102×1000m2×13600\Rightarrow x=\frac{11.2 \times 10^{-2} \times 1000\, m }{2 \times 13600}
=0.41cm=0.41\, cm