To calculate the percentage error in the measurement of density, we need to consider the measurements of mass and radius of the sphere.

Given:
Mass (m) = 50g (with an accuracy of ±0.5g)
Radius (R) = 10cm (with an accuracy of ±1mm)



To calculate the density of the sphere, we need to first determine its volume. The volume of a sphere is given by the formula:

V = (4/3)πR³

Substituting the given value of the radius (R = 10cm) into the formula, we can calculate the volume.

V = (4/3)π(10cm)³
V = (4/3)π(1000cm³)
V = 4000/3π cm³

Now that we know the volume, we can calculate the density using the formula:

Density (ρ) = mass/volume

Substituting the given value of the mass (m = 50g) and the calculated value of the volume, we can calculate the density.

Density (ρ) = 50g / (4000/3π cm³)
Density (ρ) = 150π/4000 g/cm³
Density (ρ) = 0.0375π g/cm³
Density (ρ) ≈ 0.117 g/cm³ (approximated to three decimal places)



Now that we have calculated the density, we can determine the percentage error in the measurement.

Percentage error in mass = (error in mass / actual mass) * 100
Percentage error in mass = (0.5g / 50g) * 100
Percentage error in mass = 1%

Percentage error in radius = (error in radius / actual radius) * 100
Percentage error in radius = (1mm / 10cm) * 100
Percentage error in radius = 1%

Using the calculated values above, we can determine the overall percentage error in the measurement of density.

Percentage error in density = (percentage error in mass + percentage error in volume)
Percentage error in density = (1% + 1%)
Percentage error in density = 2%

Therefore, the percentage error in the measurement of density is 2%.



The percentage error in the measurement of density is determined by considering the individual percentage errors in the measurements of mass and radius. The percentage error in each measurement is calculated by dividing the error (the given accuracy) by the actual value and multiplying by 100.

Once the individual percentage errors are determined, they are added together to obtain the overall percentage error in the measurement of density.

In this case, the percentage error in mass is 1% and the percentage error in radius is 1%. Therefore, the overall percentage error in the measurement of density is 2%.

It is important to consider the accuracy of measurements when calculating derived quantities like density. The accuracy of the final result depends on the accuracy of the individual measurements and the mathematical operations involved in the calculations.