Learn Russian: Этот город похож на столицу.

The short adjective похож (similar to / looks like) always teams up with the preposition на followed by the Accusative case. Since столица (capital) is a feminine noun ending in -а, it changes to столицу in the Accusative.

Why do we use the short form похож instead of the regular adjective похожий?

We use the short form because it acts as the main verb or state of the sentence. In Russian, when stating 'A is similar to B' or 'A looks like B', you use the short form похож. You would only use the long form похожий to directly describe a noun, like in похожий город (a similar city).

If we were talking about a country instead of a city, would похож change?

Yes! Short-form adjectives still have to match the gender and number of the subject. Because город (city) is masculine, we use похож. If the subject were feminine, like страна (country), you would use the feminine form похожа: Эта страна похожа на...

Does похож на only refer to physical appearance?

Not always. While it often means physical resemblance ('looks like'), it is also the standard way to say 'is similar to' or 'acts like' in a broader sense. In this sentence, the city might physically look like a capital, or it might just have the busy, developed vibe of one.