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Question

# In problem 10.9, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)

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Solution

## Height of the water column, h1=10+15=25cm Height of the spirit column, h2=12.5+15=27.5cm Density of water, ρ1=1gcm–3 Density of spirit, ρ2=0.8gcm–3 Density of mercury = 13.6gcm–3 Let h be the difference between the levels of mercury in the two arms. Pressure exerted by height h, of the mercury column: =hρg=h×13.6g.........(i) Difference between the pressures exerted by water and spirit: =h1ρ1g−h2ρ2g =g(25×1−27.5×0.8)=3g.....(ii) Equating equations (i) and (ii), we get: 13.6 hg = 3g h=0.220588≈0.221cm Hence, the difference between the levels of mercury in the two arms is 0.221 cm.

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