A clock with an iron pendulum keeps the correct time at 14^ C . If the room temperature is 20^ C , the error in a second per day will be nearly (coefficient of linear expansion of iron is 1.2 10⁻⁵ / ^ C )

Step-by-step solution

The time period of a simple pendulum is given by T = 2 L g Fractional change in time period due to temperature change is T T = 1 2 Error in time per day is t = 1 2 t where t = 24 60 60 = 86400 s Given = 1.2 10⁻⁵ / ^ C and = 20^ C - 14^ C = 6^ C Substituting the values: t = 1 2 1.2 10⁻⁵ 6 86400 t = 3.6 10⁻⁵ 86400 = 3.1104 s The error per day is approximately 3.11 s . Answer: 3.11 s