Final answer:
By dividing the mass of mercury by its density and rearranging the volume formula for a cylinder to solve for the radius and diameter, we find the diameter of the tube to be approximately 0.93 cm.
Step-by-step explanation:
To calculate the diameter of the cylindrical glass tube filled with mercury (Hg), we need to use its mass and the known density of mercury. First, we find the volume of mercury by dividing the mass by its density. Then, using the volume of a cylinder formula, we solve for the radius and double it to find the diameter:
Volume of Hg = mass / density = 105.5 g / 13.6 g/ml = 7.75735 ml.
Since the volume (V) of a cylinder is given by V = πr^2h, where r is the radius and h is the height (length), we can rearrange to solve for r:
r = √(V / (πh)) = √(7.75735 ml / (π * 12.7 cm)) = √(7.75735 ml / (3.1416 * 12.7 cm)) = 0.4675 cm.
The diameter (d) is 2r, which equals approximately 0.935 cm when rounded to three significant figures. This corresponds to option (a) 0.93 cm.