Discussion
Work index in size reduction can be obtained by multiplying Bond’s energy constant with
Answer: B
The work index is obtained by multiplying Bond's constant by \(\sqrt{10}\).
Bond's law gives the energy for size reduction as \(E = K_{b}\left(1/\sqrt{D_{p}} - 1/\sqrt{D_{f}}\right)\), with sizes in mm. The work index \(W_{i}\) is defined as the energy needed to reduce unit mass from a very large size (\(D_{f} \to \infty\)) to 100 µm, that is \(D_{p} = 0.1\) mm:
\[ \begin{aligned} W_{i} &= K_{b}\,\frac{1}{\sqrt{0.1}} \\ &= K_{b}\sqrt{10} \end{aligned} \]
This is the familiar relation \(K_{b} = 0.3162\,W_{i}\). Multiplying by 10, or by the cube or fourth root of 10, does not follow from the square-root form of Bond's law.
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