In a U-tube containing water and spirit separated by mercury (specific gravity of spirit = $0.8$, me

Question

In a U-tube containing water and spirit separated by mercury (specific gravity of spirit = $0.8$, mercury = $13.6$), the initial heights are $10.0	ext{ cm}$ water and $12.5	ext{ cm}$ spirit. If $15.0	ext{ cm}$ of water and spirit each are further poured into their respective arms, what is the new difference in the levels of mercury?

Professor PC Thomas Classes · Answer

Total water $h_w = 25	ext{ cm}$, total spirit $h_s = 27.5	ext{ cm}$. Pressure difference before mercury shifts: $P_{diff} = ho_w g h_w - ho_s g h_s = (1 	imes 25 	imes g) - (0.8 	imes 27.5 	imes g) = 3g$ (in cm of water). This is balanced by mercury: $ho_{Hg} g h = 3g \implies 13.6 h = 3 \implies h \approx 0.22	ext{ cm}$.