Question

Pendulum of a clock consists of very thin sticks of iron and an alloy. At room temperature the iron sticks 1 and 2 have length `L_0` each. Length of each of the two alloy sticks 4 and 5 is 0 and the length of iron stick 3 (measured up to the centre of the iron bob) is `l_0`. Thickness of connecting strips are negligible and mass of everything except the bob is negligible. The pendulum oscillates about the horizontal axis shown in the figure. It is desired that the time period of the pendulum should not change even if temperature of the room changes. Find the coefficient of linear expansion (`alpha`) of the alloy if the coefficient of linear expansion for iron is `alpha_(0)`.

Answer 1

Correct Answer - `alpha=((L_(0)+lambda_(0))alpha_(0))/(l_(0))`