A wire has a mass (0.3 ±0.003) g, radius (0.5+0.005) mm and length (6 ±0.06) cm. The maximum per

step 1 In this question we have del m by m is equal to 0 .003 divide by 0 .3 and del r by r is equal to

A wire has a mass (0.3 ±0.003) g, radius (0.5+0.005) mm and...

A wire has a mass $(0.3 \pm 0.003) \mathrm{g}$, radius $(0.5+0.005) \mathrm{mm}$ and length $(6 \pm 0.06) \mathrm{cm}$. The
maximum percentage error in the measurement of its density is $\quad$ IITT JEE 2004]
(a) 1
(b) 2
(c) 3
(d) 4

Key Concepts

Error Propagation

Error propagation is the process of determining the uncertainty of a result derived from multiple measurements, each with their own uncertainties. When quantities are combined through multiplication, division, or raised to a power, their relative errors add (taking into account the power factors) to provide the overall relative error in the computed result.

Density Calculation

Density is defined as mass divided by volume. When calculating the density of an object, uncertainties in both mass and volume measurements contribute to the final uncertainty. Special attention is required for volume if it depends on measurements raised to a power, as errors in those measurements have a magnified effect on the uncertainty of the volume and, consequently, the density.

Measurement Uncertainty

Measurement uncertainty is the doubt that exists about the result of any measurement. It quantifies the variability or possible error in the measurement process and is typically given as an absolute error (e.g., ± value) alongside the measured value.

Relative Error

Relative error expresses the uncertainty of a measurement relative to the size of the measurement itself, typically represented as a fraction or percentage. It is calculated by dividing the absolute error by the measured value, and it helps to compare the accuracy of measurements taken on different scales.

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