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The statistical analysis of the length distribution of catalytic chemical vapour deposition synthesized multi-walled carbon nanotubes cut by planetary ball milling is reported. The nanotube lengths follow a log-normal distribution in a broad range of grinding time and rotational speed. We show that the scale parameter of the distribution, which equals the mean of the natural logarithm of the tube lengths, decreases linearly with the product of the duration time and the rotational speed. This relation can be used for tailoring nanotube lengths by a suitable choice of process parameters for a wide range of applications.