
Concept explainers
A proton has a radius of approximately
a. Determine the density of a proton. For a sphere,
b. By assuming that black holes have the same density as protons, determine the mass (in kilograms) of a black hole and the size of a sand particle. A typical sand particle has a radius of

Interpretation:
The density of a proton and the mass of a black hole is to be calculated.
Concept Introduction:
Density of a substance is a measure of compactness of that substance. It is defined as the mass of a substance present in per unit of its volume. The unit of density is derived when the unit of mass is divided by the unit of volume. Its most common units are
Answer to Problem 46E
Solution: a)
Explanation of Solution
a) The density of a proton having radius of approximately
Calculation of volume of a proton is as:
Substitute the given values in the above equation as:
Therefore, the volume of a proton is
Calculation of density of a proton is as follows:
Substitute the given values in the above equation as:
Thus, the density of a proton is
b) The mass of a black hole and the size of a sand particle, radius of sand particle is
The volume of a black hole is as follows:
So,
Substitute the given values in the above equation as:
Thus, the volume of the black hole is
The calculation of mass of the black hole is as follows:
Substitute the values in the above equation as:
Conversion of grams into kilograms is as follows:
Hence, the mass of the black hole is
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Chapter 2 Solutions
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