To solve this question, we will use the formula for linear expansion, which is given by: ΔL = L0 * α * ΔT where: - ΔL is the change in the length of the rail, - L0 is the initial length of the rail, - α is the linear expansion coefficient of the material, - ΔT is the temperature change. Let's follow the steps: 1. Identify the initial length (L0) of the rail, which is 10 m. Since we want the answer in millimeters, we will convert to millimeters by multiplying by 1000, giving us L0 = 10 * 1000 = 10000 mm. 2. Note the linear expansion coefficient (α) of the metal, which is 3.0 x 10^-5 °C^-1. 3. Calculate the temperature change (ΔT), which is the final temperature minus the initial temperature. The final temperature is 35°C and the initial is 20°C, so ΔT = 35 - 20 = 15°C. 4. Apply the formula for linear expansion to find the change in length (ΔL): ΔL = 10000 mm * 3.0 x 10^-5 °C^-1 * 15°C = 4.5 mm. 5. Add the change in length (ΔL) to the initial length (L0) to get the final length (Lf): Lf = 10000 mm + 4.5 mm = 10004.5 mm. Therefore, the length of the rail on a day with a temperature of 35°C will be 10004.5 mm, which corresponds to option (c).