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Units and Measurements — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements5 Marks
Question
In an experiment on determining the density of a rectangular block, the dimensions of the block are measured with a Venier Caliper (with a least count of 0.01cm) and its mass is measured with a beam balance of least count of 0.1gm. How do we report our result for the density of the block?
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Answer

Let the measured values be: Mass the block (m) = 39.3g length (l) = 5.12cm breadth (b) = 2.56cm thickness (t) = 0.37cm The density of the block is given by: $\text{d}=\frac{\text{mass}}{\text{volume}}=\frac{\text{m}}{\text{l}\text{ ,b}\text{ ,h}}$ $=\frac{39.3}{5.12'2.56'0.37}=8.1037\text{gram}/\text{ cm}^3$ Now the uncertain value are: $\text{l}=\pm0.01\text{cm}$ $\text{b}=\pm0.01\text{cm}$ $\text{t}=\pm0.01\text{cm}$ Maximum relative error, in the density, value is given by: $\frac{\text{Dd}}{\text{d}}=\frac{\text{Dl}}{\text{l}}+\frac{\text{Db}}{\text{b}}+\frac{\text{Dt}}{\text{t}}+\frac{\text{Dm}}{\text{m}}$ $=\frac{0.01}{5.12}+\frac{0.01}{2.56}+\frac{0.01}{0.37}+\frac{0.7}{39.3}$ $=0.0019+0.0039+0.027+0.0024=0.0358$ $\therefore\Delta\text{d}=0.358\times8.1037=0.3\text{g}/\text{cm}^3\text{approx}$

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