I started the experiment by measuring the diameter of the wire, using the micrometer screw gauge. Before starting the measurement I checked for an error in the screw gauge. My gauge had a 0.002 cm positive error, which I had to subtract from my readings. I put the wire in the clamp of the gauge and tightened it, then I took note of the reading on the circular scale. I repeated this four more times (to get an accurate answer), then subtracted 0.002cm from each of the reading and then took an average of all the readings giving me the true value of the diameter of the wire. The error in this case is half of the least count. Since the LC of the screw gauge is 0.001cm the error is +/- 0.0005cm.
Next I calculated the mass of the wire with the help of a digital weighing balance. Firstly I “reset” the balance, then I placed the wire inside and shut the glass protector. This helps to give us more accurate readings because it curbs the influence of air on the balance. I then took note of the reading and repeated this four times. Then I took the average of the readings to get the true value of the weight (in grams). The error in this case is equal to the least count of the instrument (as it is electronic). Thus the error in this case is equal to +/- 0.001 grams.
The final value needed for the density was the length. Since the wire was not exactly straight, length had to be calculated with the help of a string and a ruler. I lined the string with the wire, made a mark on it and measure it with the help of a ruler. After repeating this four times and after taking the mean of all the measurements, I got the true value of the length. The error (being half of the LC of ruler) was +/- 0.005cm.
Assuming that the wire was a cylinder, I calculated the volume using the formulae πr2h. The height here is the length. Substituting the respective values I got the volume as 0.00577 cm3. Next I used the formula Density = Mass/Volume. Again by substituting the values I got the density as 9.61 g/cm3.
Now for the uncertainties. To get the uncertainties of density, I first calculated the percentage error of the diameter, height and mass. The percent error of diameter is the uncertainty of d by the diameter, multiplied by 100. Similarly I calculated the percentage errors the height and mass as 0.66% and 0.18%, respectively. The percent error of diameter is 5.05%.