Chemistry - Heating of Ethers with HI and Cleavage of Ethers

Solution 1:

Your ether has $\ce{CH2}$ groups at both sides of the oxygen atom.

I would exclude a $S_N1$ reaction here! Instead, cleavage of the ether proceeds via $S_N2$. The oxonium ion resulting from addition of a proton is attacked by iodide at the least hindered carbon atom. Iodide is quite big ;-)

Solution 2:

According to me, The product should be this due to delocalisation of positive charge among the neighbouring Carbon atoms.

Even if you consider an $S_N1$ reaction pathway for this reaction, the positive charge could be more stable on the $\ce{-CH2CH3}$ branch as it has three hyperconjugation structures stabilizing the positive charge against one in the other branch. And gives the same products.

Moreover, as Klaus Warzecha said, steric hindrance comes into the play while considering $S_N2$ pathway which looks a more plausible pathway due to the relatively unstable primary carbocations that form in $S_N1$