Question

A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. 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)

Answer 1

The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other.

thus, density of spirit , $\rho_s$=10cm/12.5cm × 1g/cm³ = 0.8 g/cm³

Let x is the difference in the level of mercury in the two arms , on adding 15cm of water and 15cm of spirit in respective arms of the tube.

now, pressure due to (10 + 15)cm or 15cm of water = pressure due to x cm of mercury + pressure due to (12.5 + 15) or 27.5cm of spirit

$\rho_wh_wg=\rho_{hg}xg+\rho_sh_sg$

or, $\rho_wh_w=\rho_{hg}x+\rho_sh_s$

or, 25cm × 1g/cm³ = 13.6 g/cm³ × x + 0.8 g/cm³ × 27.5

or, x = (25 - 0.8 × 27.5)/13.6 = 0.221cm

hence, answer is 0.221cm