1. **Stating the problem:** We have two questions here: - Which pair of statements about combining uncertainties is true? - For a 0.50 kg mass suspended in equilibrium with a string at 60° to the horizontal, find the tension in the horizontal string. 2. **Combining uncertainties:** - When quantities are multiplied or divided, **percentage (relative) uncertainties are added**. - When quantities are added or subtracted, **absolute uncertainties are added**. Therefore, for subtraction, absolute uncertainties are added; for division, percentage uncertainties are added. 3. **Answer to uncertainty question:** - Option D states: "Absolute uncertainties are added" for subtraction and "Percentage uncertainties are added" for division, which is correct. 4. **Physics problem setup:** - Mass $m = 0.50$ kg - Gravitational acceleration $g = 9.8$ m/s$^2$ - Weight force $W = mg = 0.50 \times 9.8 = 4.9$ N - The system is in equilibrium, so forces balance. - The angled string makes $60^\circ$ with the horizontal. 5. **Forces analysis:** - Let $T_h$ be the tension in the horizontal string. - Let $T_a$ be the tension in the angled string. 6. **Vertical force balance:** - Vertical component of angled string tension balances weight: $$T_a \sin 60^\circ = W = 4.9$$ $$T_a = \frac{4.9}{\sin 60^\circ} = \frac{4.9}{\frac{\sqrt{3}}{2}} = \frac{4.9 \times 2}{\sqrt{3}} \approx 5.65 \text{ N}$$ 7. **Horizontal force balance:** - Horizontal components of tensions must balance: $$T_h = T_a \cos 60^\circ = 5.65 \times \frac{1}{2} = 2.825 \text{ N}$$ 8. **Final answer:** - The tension in the horizontal string is approximately $2.8$ N. - Closest option is B. 2.9 N. **Summary:** - True uncertainty statement: D - Tension in horizontal string: B (2.9 N)