Will a Ball placed close to Sun fall into it?
Short answer is yes. The only way radiation pressure would be a factor was if the ball was in orbit around the Sun, this would mean that the slight pressure it feels would cause it to drift away slowly (assuming its made of the most heat resistant material on Earth!). But in your question you said "placed" near the sun not in orbit around it, so the strength of the sun's gravity would overcome all other forces and pull it in.