The density of a material in SI units is 128 kg m-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is
Question
The density of a material in SI units is 128 kg m-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is
Solution
To convert the density from SI units to the given units, we need to convert the mass from kg to g and the length from m to cm.
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Convert mass from kg to g: 1 kg = 1000 g So, 128 kg = 128 * 1000 g = 128000 g
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Convert length from m to cm: 1 m = 100 cm So, 1 m^3 = 100 cm * 100 cm * 100 cm = 1000000 cm^3
Therefore, the density in g/cm^3 is 128000 g / 1000000 cm^3 = 0.128 g/cm^3
Now, we need to convert this to the units where the unit of length is 25 cm and the unit of mass is 50 g.
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Convert mass from g to 50g units: 1 unit of mass = 50 g So, 0.128 g = 0.128 / 50 mass units = 0.00256 mass units
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Convert length from cm^3 to (25 cm)^3 units: 1 unit of length = 25 cm So, 1 cm^3 = 1 / (252525) length units = 0.000064 length units
Therefore, the density in the given units is 0.00256 mass units / 0.000064 length units = 40 mass units/length units.
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