The density of a material in the shape of a c | vedclass

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(B) Density $(d)$ is given by the formula: $d = \frac{M}{V} = \frac{M}{L^3}$,where $M$ is the mass and $L$ is the length of the side of the cube.Using

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$4.5$

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(B) Density $(d)$ is given by the formula: $d = \frac{M}{V} = \frac{M}{L^3}$,where $M$ is the mass and $L$ is the length of the side of the cube.Using the propagation of errors formula,the relative error in density is given by: $\frac{\Delta d}{d} = \frac{\Delta M}{M} + 3 \frac{\Delta L}{L}$.Given that the relative error in mass $\frac{\Delta M}{M} = 1.5\%$ and the relative error in length $\frac{\Delta L}{L} = 1\%$.Substituting these values into the equation: $\frac{\Delta d}{d} = 1.5\% + 3(1\%) = 1.5\% + 3\% = 4.5\%$.Therefore,the maximum error in determining the density is $4.5\%$.

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 ........ $\%$

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