1. **State the problem:** An object is suspended from a scale inside an elevator accelerating upwards at $1.25\ \text{m/s}^2$. The scale reads a mass of 45 kg. We need to find the true mass of the object. 2. **Relevant formula:** The scale measures the apparent weight, which changes due to acceleration. The apparent weight $W_{apparent}$ relates to true mass $m$ and acceleration $a$ by: $$W_{apparent} = m(g + a)$$ where $g = 9.8\ \text{m/s}^2$ is gravitational acceleration. 3. **Convert scale reading to force:** The scale reading in kg can be converted to force (weight) by multiplying by $g$: $$F_{apparent} = 45 \times 9.8 = 441\ \text{N}$$ 4. **Use the formula to find true mass:** Rearranging the formula: $$m = \frac{F_{apparent}}{g + a}$$ Substitute values: $$m = \frac{441}{9.8 + 1.25} = \frac{441}{11.05} \approx 39.91\ \text{kg}$$ 5. **Interpretation:** The true mass of the object is approximately 39.91 kg, less than the apparent mass due to the elevator's upward acceleration. **Final answer:** The true mass of the object is approximately **39.91 kg**.