Chemistry - What will be the Ozonolysis product?

Solution 1:

There are two types of control, that governs reaction path:

• kinetic control (path with least activation energy) and
• thermodynamic control (path with least energy of products).

Given temperature favors kinetic control.

Ozonolysis starts as 2+3 electrocyclic addition (with later regroup of the product), similar to Diels-Alder reaction . Please, read about this reaction in good organic chemistry textbook, especially about what controls geometry of products, it will help to understand what I'm going to say next.

Ozone has low energy of LUMO, so alkene part here provides HOMO, that is still lower then Ozone's LUMO. Oxygen from $OMe$ group donates some electronic density to $C-C$ double bound, so this bond becomes more active, then opposite one.

Solution 2:

Any reaction in general will try to attain maximum possible stability.
The reactivity of a molecule or a group is inversely proportional to its stability.
The general order of reactivity of carbonyl compounds is as follows:

$$\small\ce{Aldehyde > Ketone > Acid halide > Anhydride > Ester > Carboxylic Acid > Acid Amide}$$ (Reference)

So if the left bond breaks it results in a ketone which is more reactive(hence less stable) as compared to the product formed by the cleavage of the right bond which is an ester.
Hence the bond on the right would break to form an ester.