The main question is why? Well, because by installing the second disc of Grand Theft Auto 5 the game will actually work worse than the uninstalled version of the game.
“For optimal performance, we recommend not installing that disc,” Rockstar wrote. “We will have more info on our Support Site at launch.” they added.
Apparently, you only need to install the first disc, while the second disc (the play one) should stay uninstalled. This will prevent you from seeing a lot of pop-up graphics in the game and textures appearing and disappearing.