A rod’s shape is position $\mathbf r(s)$ at arclength s, 0≤s≤l. Its bending energy is $E=K\int_0^l\left|\partial^2\mathbf r/\partial s^2\right|^2ds$. Find dimensions of K.
Position has length dimension, and differentiating twice by arclength leaves dimension L⁻¹. Squaring and integrating over ds gives L⁻¹. Since energy has dimension ML²T⁻², K must have dimension ML³T⁻² to compensate. Thus B.
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