The amplitude and phase angle due to original unbalance in a grinding wheel operating at \(1200 \mathrm{rpm}\) are found to be \(0.25 \mathrm{~mm}\) and \(40^{\circ}\) counterclockwise from the phase mark. When a trial mass \(m=170 \mathrm{~g}\) is added at \(65^{\circ}\) clockwise from the phase mark and at a radial distance \(65 \mathrm{~mm}\) from the center of rotation, the amplitude and phase angle are observed to be \(0.5 \mathrm{~mm}\) and \(150^{\circ}\) counterclockwise. Find the magnitude and angular position of the balancing weight if it is to be located \(65 \mathrm{~mm}\) radially from the center of rotation.