We show that the notion of the maximum force conjecture $F leqslant 1/4$ in general relativity, when applied to asymptotically flat singly spinning Myer-Perry black holes in any dimension, reveals the underlying thermodynamic instability in a number of ways. In particular, the Hookean force law $F_1=kx$, suitably defined, is bounded by the conjectured limit, but in $dgeqslant 6$ it is further bounded by a dimensional dependent value less than $1/4$, which remarkably corresponds to the Emparan-Myers fragmentation (splitting of a black hole into two becomes thermodynamically preferable). Furthermore, we define another force as the square of the angular momentum to entropy ratio ($F_2=J^2/S^2$). In dimensions $dgeqslant 6$, the positive Ruppeiner scalar curvature region in the thermodynamic phase space is marked by the upper boundary $F_2=frac{1}{12}left(frac{d-3}{d-5}right)$ and the lower boundary $F_2=frac{1}{4}left(frac{d-3}{d-5}right)$, the latter corresponds to a black hole that suffers from Gregory-Laflamme instability. Surprisingly, the upper and lower boundaries correspond to $F=1/4$ when $d=6$ and $dto infty$, respectively. We discuss how the maximum force may be relevant to the underlying black hole microstructure and its relationship to cosmic censorship.
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