Question

U-tube contains some Mercury of a relative density 13.6
(a) kerosene of relative density 0.8 is poured into one arm of the U-tube until the height of Mercury in that arm is reduced by 1.5cm. calculate the height of kerosene
(b) Water is now poured into the other arm of the U-tube until the levels of Mercury in both arms are again the same. Calculate the height of the water column. (Density of water = 1gcm^-3

Answer 1

(a) The pressure must be equal in both arms:

$$\rho_kgh_k=\rho_mg\Delta h_m,\\\space\\ h_k=\Delta h_m\frac{\rho_m}{\rho_k}=25.5\text{ cm}.$$

(b) When the levels of mercury are the same, we can ignore its presence and weights forces created by the kerosene and water only:

$$\rho_kgh_k=\rho gh,\\\space\\ h=h_k\frac{\rho_k}{\rho}=20.4\text{ cm}.$$