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Mechanical Properties Of Solids

Question

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

6%

2.5%

3.5%

4.5%

Solution

4.5%

Density = Mass/Volume

$\frac{I ∆ d}{d} = \frac{I ∆ M}{M} + \frac{3 ∆ L}{L} = 1.5 + 3 (1) = 4.5 %$