Problem: The radius of a uniform solid sphere is measured to be (6.50 ± 0.20) cm and its mass is measured to be (1.85 ± 0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

FREE Expert Solution

We're asked to determine the density and its uncertainty for a sphere given its radius and mass.

For operations with uncertainty, we’ll follow two different rules depending on whether we're adding/subtracting or multiplying/dividing:

  • When measurements are added or subtracted, sum the absolute or relative uncertainty—the result is the same. 
  • When measurements are multiplied or divided, sum the relative uncertainties.

So anytime you square a measurement, add the uncertainty twice (three times for a cubed measurement).

To convert between absolute uncertainty and relative uncertainty, we’ll use this formula (m=measurement, Δu=absolute uncertainty):

m±u=m±(um)

We'll cover mass and density more in a later video, but you may already know that density is mass over volume, ρ = m/V (ρ is the Greek letter"rho"). 

The volume of a sphere is given by 

V=43π r3.

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Problem Details

The radius of a uniform solid sphere is measured to be (6.50 ± 0.20) cm and its mass is measured to be (1.85 ± 0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Uncertainty concept. If you need more Uncertainty practice, you can also practice Uncertainty practice problems.

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Based on our data, we think this problem is relevant for Professor Pandit's class at USF.