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Here is the center of mass of a solid cone and a hollow cone along with the derivation.

Here is the center of a solid hemisphere and that of a hollow hemisphere along with its derivation

Here is the center of mass of a triangular lamina, along with the derivation

Here is the center of mass of a semicircular and an annular semicircular disc along with its derivation

Here is the center of mass of a uniform circular arc along with its derivation.

Here is the center of mass of an arc of a ring and that of a semicircular ring, along with their derivation.

Here is the center of mass of a non uniform rigid body (rod of length L). Note that the approach / derivation hass also been provided.

Here is the center of mass of an I shaped lamina along with its derivation

Here is the center of mass of two or more particle systems that you can expect to come across in JEE Main and JEE Advanced

https://vimeo.com/574748184