Four holes are drilled in a uniform circular disc at a radius of \(100 \mathrm{~mm}\) and angles of \(0^{\circ}, 60^{\circ}\), \(120^{\circ}\), and \(180^{\circ}\). The weight removed at holes 1 and 2 is \(100 \mathrm{~g}\) each and the weight removed at holes 3 and 4 is \(150 \mathrm{~g}\) each. If the disc is to be balanced statically by drilling a fifth hole at a radius of \(125 \mathrm{~mm}\), find the weight to be removed and the angular location of the fifth hole.