A pendulum clock loses 12 s a day if the temperature is 40 o C and gains 4s a day if the temperature is 20 o C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion α of the metal of the pendulum shaft are respectively:

Step-by-step solution

∆ T T = 1 2 ∆ l l = 1 2 α ∆ θ   12 4 = 40 - θ θ - 20 3 θ - 60 = 40 - θ 4 θ = 100 θ = 25 o C Also, ∆ T = 1 2 α   ∆ θ × T 4 = 1 2 α   5 × 86400 8 5 × 86400 = α α = 1.85 × 10 - 5 / o C