The time period of a simple pendulum made using a thin copper wire of length L is T. Suppose the temperature of the room in which this simple pendulum is placed increases by 30°C, what will be the effect on the time period of the pendulum ?

The time period (T) of a simple pendulum is governed by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity [1]. When the temperature of the room increases by 30°C, the thin copper wire undergoes linear thermal expansion. According to the principle of thermal expansion, the change in length (ΔL) is proportional to the original length, the temperature change (Δθ), and the coefficient of linear expansion (α), expressed as ΔL = LαΔθ. As the temperature rises, the copper wire expands, increasing the length L of the pendulum. Since the time period T is directly proportional to the square root of the length, an increase in length results in a slight increase in the time period. Therefore, the pendulum will take more time to complete one oscillation, causing the period T to increase slightly.

Sources

1. [1] https://en.wikipedia.org/wiki/Pendulum