Question

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 1

`\rho = 2.39 g/mL`

`\Delta \rho = 1.53 * 10^(-3) mL`

Step-by-step explanation:

As we know that density is the ratio of mass and volume of the object

here we know that

mass of the rock is

`m = 750 g`

volume of the rock is given as

`V = V_1 - V_o`

here we know that

`V_1 = 813.2 \pm 0.1 mL`

`V_2 = 500.0 \pm 0.1 mL`

now we have

`V = 313.2 \pm 0.2 mL`

now density is given as

`\rho = (750)/(313.2)`

`\rho = 2.39 g/mL`

now uncertainty of density is given as

`\Delta \rho = (\Delta V)/(V) \rho`

`\Delta \rho = (0.2)/(313.2)(2.39)`

`\Delta \rho = 1.53 * 10^(-3) mL`