An unbalanced flywheel shows an amplitude of \(0.165 \mathrm{~mm}\) and a phase angle of \(15^{\circ}\) clockwise from the phase mark. When a trial weight of magnitude \(50 \mathrm{~g}\) is added at an angular position \(45^{\circ}\) counterclockwise from the phase mark, the amplitude and the phase angle become \(0.225 \mathrm{~mm}\) and \(35^{\circ}\) counterclockwise, respectively. Find the magnitude and angular position of the balancing weight required. Assume that the weights are added at the same radius.