Thank you for the opportunity to help you with your question!

We use the formula of the volume of a cylinder which is:

V = A*h

So the area of the right arm (where the water is) is A2 = 4.70 cm^2 and it is also given the mass of that column of water which is 100 grams. Then from the above formula we solve for h like this:

V = A2*h --------> V/A2 = A2*h/A2 ---------> V/A2 = h

So we need to determine the volume of the water. For that, we use the formula of the density and solve for V:

d = m/V --------> d*V = m ----------> V = m/d

The density of the water is known, it is approximately 1 gram/cm^3. Then we would have:

V = 100 grams/ 1gram/cm^3 = 100 cm^3 ---------> V = 100 cm^3

So then we have:

h = V/A2 = 100 cm^3/ 4.70 cm^2 -----------> h = 21.2765 cm -------> h = 21.28 cm

I need a little bit more time to get part B. But please let me know if you have any doubt or question about part A.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Jun 11th, 2015

By the Arquimides principle, then if we have 100 grams of water on the right arm because of that column of water the the mercury rises a distance h, so it will be displaced 100 grams of mercury. Therefore, the volume of mercury would be:

d = m/V -----> V = m/d -----> V = 100 grams/13.6 grams/cm^3 --------> V = 7.353 cm^3

V = A1*h -----> h = V/A1 = 7.353 cm^3/ 10.2 cm^2 ----------> h = 0.72 cm