# Ring expansion in cyclic compounds

My attempt

In the first case:
$\ce{H+}$ adds to the $\ce{OH}$ group, giving us a carbocation. The carbocation thus formed is exceptionally stable due to back bonding. I wonder why would it go under ring expansion even though the strain is not a factor here as the ring strain in a cyclobutane ring is ~$26.3\ \mathrm{kcal/mol}$, and that in a cyclopropane ring is ~$27.5\ \mathrm{kcal/mol}$.

In the second case:
Again the $\ce{H+}$ adds to the $\ce{OH}$ group, giving us a tertiary carbocation with seven hyper-conjugating structures. Why would it go under ring expansion to give secondary carbocation with just two hyper-conjugating structures? I believe is based on ring strain in this case, as the ring strain in a five-membered ring is ~$6.2\ \mathrm{kcal/mol}$, while the ring strain in a six-membered ring is ~$0.1\ \mathrm{kcal/mol}$.

Source: Advanced Problems In Organic Chemistry, MS Chouhan, 11th edition; Chapter - Hydrocarbons (Alkenes); Question 180 in latest edition

• I will expect the carboncation after ring contraction reaction to be trapped by some nucleophile instead of elimination product. With no $sp^{2}$ carbon center involved in the product, the ring strain data will make sense in this case. Thus, resonance structure stabilization will overcome the ring strain. This reaction should be a reaction somewhat under kinetic condition with careful control, and it may not happen under general thermodynamic condition(just heat up without any nucleophile), where I will expect ring opening to happen. – Ian Fang Jun 13 '15 at 14:33