Final answer:
To find the equivalent mercury column height to a 12 cm tall water column, divide the water column height by 13.6. The correct height of the mercury column is approximately 0.88 cm.
Step-by-step explanation:
To find the equivalent height of a mercury column that corresponds to a 12 cm tall column of water, given the density of water is 1.00 g/ml and the density of mercury is 13.6 g/ml, we use the fact that the hydrostatic pressure exerted by the columns of water and mercury must be equal at equilibrium. Since the density of mercury is 13.6 times greater than the density of water, the height of the mercury column will be 1/13.6 times the height of the water column, to exert the same pressure. Calculating this we get Hmercury = Hwater / 13.6, Hmercury = 12 cm / 13.6, Hmercury = 0.8824 cm. Therefore, the equivalent mercury column height is approximately 0.88 cm, which corresponds to answer choice (a).