Problem 9E

The density of a rock will be measured by placing it into a graduated cylinder partially filled with water, and then measuring the volume of water displaced. The density D is given by D = m/( V1 – V0), where m is the mass of the rock, V0 is the initial volume of water, and V1, is the volume of water plus rock. Assume the mass of the rock is 750 g, with negligible uncertainty, and that V0 = 500.0 ± 0.1 mL and V1 = 813.2 ± 0.1 mL. Estimate the density of the rock, and find the uncertainty in the estimate.

Answer :

Step 1 of 2 :

Given,

The density of a rock will be measured by placing it into a graduated cylinder partially filled with water and then measuring the volume of water display.

D is the density, D = ,

Where, m = mass of rock,

= initial volume of water

= volume of water plus rock.

We have to assume that the rock is 750g, with negligible uncertainty

And = 500.0 0.1 ml and =813.2 0.1 ml

The claim is to estimate the density of the rock and the uncertainty in the estimate.