Final answer:
The largest possible percentage of error in the density reading of the wire, taking into account mass, radius, and length uncertainties, is 4%.
Step-by-step explanation:
To find the largest possible percentage of error in a density reading, we need to consider the uncertainties in the mass, radius, and length measurements of the wire. Density (ρ) is defined as the mass (m) of an object divided by its volume (V). The volume of a cylinder (like a wire) is given by V = πr2h, where r is the radius and h is the height (or length of the wire in this case). The formula for the density of the wire thus becomes:
ρ = m / (πr2h)
To calculate the maximum percentage error in the density, we add the relative errors of each measurement. We assume that errors are independent and add them as follows:
Percentage error in density = (Relative error in mass + 2 × Relative error in radius + Relative error in length) × 100%
Applying the given values:
Percentage error in mass = (0.004 g / 0.4 g) × 100% = 1%
Percentage error in radius = (2 × 0.005 mm / 0.5 mm) × 100% = 2%
Percentage error in length = (0.06 cm / 6 cm) × 100% = 1%
The maximum possible percentage error in the density reading will therefore be:
Maximum percentage error = (1% + 2% + 1%) = 4%