Final answer:
The period of oscillation of a pendulum clock can change due to the thermal expansion of the pendulum material. By calculating the change in length of the pendulum using the coefficient of linear expansion, we can determine the change in period. This allows us to calculate the time gained or lost in a given timeframe.
Step-by-step explanation:
The period of oscillation of a pendulum clock can change due to the thermal expansion of the material used for the pendulum. In this case, brass is used for the pendulum and the temperature changes from 35ºC to 20ºC from day to night. To determine the time gained or lost, we need to calculate the change in the period of the pendulum.
By using the equation for the change in length of a material due to temperature change, ΔL = (αLΔT), where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature, we can calculate the change in length of the pendulum.
Using the formula for the period of a pendulum, T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity, we can calculate the change in period of the pendulum based on the change in length. From there, we can calculate the time gained or lost in 12 hours.