5. A meter stick is pivoted at its \( 50-\mathrm{cm} \) mark but does not balance because of nonuniformities in its material that cause its center of gravity to be displaced from its geometrical center. However, when weights of 150 and 200 g are placed at the \( 10-\mathrm{cm} \) and \( 75-\mathrm{cm} \) marks, respectively, balance is obtained. The weights are then interchanged and balance is again obtained by shifting the pivot point to the \( 43-\mathrm{cm} \) mark. Find the mass of the meter stick and the location of its center of gravity.