Final answer:
The clock with a steel wire pendulum loses approximately 5.18 seconds in one week when the temperature is increased to 35°C due to thermal expansion of the steel, which affects the period of the pendulum.
Step-by-step explanation:
The question relates to the change in period of a pendulum clock due to thermal expansion when the temperature changes. The coefficient of linear expansion for steel (αsteel) is given as 1.2×10−5/°C. The clock shows the correct time at 25°C, but the temperature increases to 35°C. To determine the time lost or gained by the clock, we would use the formula for the change in length due to temperature change ΔL = αLΔT, where α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.
The time period of a pendulum is T = 2π√(L/g), so when the length changes, the period also changes. This change in period can be approximated as ΔT/T ≈ αΔT/2. With the change in temperature being 10°C (from 25°C to 35°C), we can calculate the fractional change in period, and then find out how much time the clock gains or loses over the course of one week.
After calculations, one can determine that the clock loses time. By plugging all known values into the formula and carrying out the calculations, we find that the clock loses approximately 5.18 seconds per week, answer option B.