A pendulum clock is 5 s fast at a temperature of 15 ° C and 10 s slow at a temperature of 30 ° C . At what temperature does it give the correct time? (take time interval = 24 hours )

Step-by-step solution

Δ t = 1 2 α Δ T × t ∴ 5 = 1 2 α T - 1 5 × 8 6 4 0 0 .........(i) And 1 0 = 1 2 α 3 0 - T × 8 6 4 0 0 ........(ii) Dividing both equations, 1 2 = T - 15 30 - T ⇒ 30 - T = 2 T - 30 ⇒ 3 T = 60 ⇒ T = 20 ° C