In an experiment on determining the density of a rectangular bloc… - Vidyadip

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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