The length, width and thickness of a block are (100.0 ±0.1) cm,(10.00 ±0.01) cm and (1.000 ±0.00

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The length, width and thickness of a block are (100.0 ±0.1)...

The length, width and thickness of a block are (100.0 $\pm 0.1) \mathrm{cm},(10.00 \pm 0.01) \mathrm{cm}$ and $(1.000 \pm 0.001) \mathrm{cm}$ respectively. The maximum possible error in its volume will be (A) $\pm 0.111 \mathrm{~cm}^{3}$ (B) $\pm 0.012 \mathrm{~cm}^{3}$ (C) $+0.03 \mathrm{~cm}^{3}$ (D) None of these

The length, width and thickness of a block are (100.0 $\pm 0.1) \mathrm{cm},(10.00 \pm 0.01) \mathrm{cm}$ and $(1.000 \pm 0.001) \mathrm{cm}$
respectively. The maximum possible error in its volume will be
(A) $\pm 0.111 \mathrm{~cm}^{3}$
(B) $\pm 0.012 \mathrm{~cm}^{3}$
(C) $+0.03 \mathrm{~cm}^{3}$
(D) None of these

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Key Concepts

Error Propagation

Error propagation is the process used to determine the uncertainty in a result calculated from multiple measurements, each with their own uncertainties. When quantities are combined to obtain a final result, their individual uncertainties affect the accuracy of that result, and error propagation techniques help calculate the overall uncertainty.

Relative and Absolute Errors

Absolute error is the uncertainty in a measurement expressed in the same units as the measurement itself, while relative error (or percentage error) is the ratio of the absolute error to the measured value. These concepts are crucial for understanding and comparing the uncertainties associated with different measurements.

Multiplicative Error Propagation

When measurements are multiplied together, such as in calculating the volume from length, width, and thickness, the relative errors add to give an approximation of the total relative error in the product. This method is used to estimate the maximum possible error in the computed volume from the relative uncertainties of each dimension.

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