Teaser 2885: Croquet mallet

From The Sunday Times, 7th January 2018 [link]

My croquet mallet is less than a metre high and consists of a cylindrical shaft attached to a heavier cuboid head, both of uniform density. Knowing the total weight of the mallet, I wanted to work out the weight of the shaft. I found the point of balance along the shaft and measured the distances from there to each end of the shaft, the smaller of which was less than the height of the head. Each of these three distances was a whole prime number of cm, and taking the three distances together with the height of the mallet, no digit was repeated. I worked out that the weight of the head was a single digit multiple of the weight of the shaft.

What was the height of my mallet?

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