Concept explainers
The radius of a solid aluminum sphere that balance a solid iron sphere on an equal arm balance.
Answer to Problem 13P
The radius of a solid aluminum sphere is
Explanation of Solution
The mass of one cubic meter aluminum is
Write the formula to calculate the density of aluminum sphere
Here,
Substitute
Write the formula to calculate the density of iron sphere
Here,
Substitute
Write the formula to calculate the mass of an aluminum sphere
Here,
Write the formula to calculate the volume of an aluminum sphere
Here,
Substitute
Write the formula to calculate the mass of a solid iron sphere of radius
Here,
Write the formula to calculate the volume of iron sphere
Here,
Substitute
Since both sphere must balance to each other on an equal arm balance. So, they both have equal mass.
Equating equation (I) and equation (II),
Conclusion:
Substituting
Therefore, the radius of a solid aluminum sphere is
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