Question

A clock with an iron pendulum keeps the correct time at 15°C. If the room temperature is 20°C, the error in seconds per day will be near ______.

(coefficient of linear expansion of iron is 1.2 × 10^-5/°C) 

Options

• 6.2 s

• 1.3 s

• 2.6 s

• 3.1 s

Answer 1

A clock with an iron pendulum keeps the correct time at 15°C. If the room temperature is 20°C, the error in seconds per day will be near 2.6 s.

Explanation:

The fractional change in the time period is given by,

`(DeltaT)/T = 1/2alphaDeltatheta ⇒ DeltaT = (TalphaDeltatheta)/2`

Here, T = 1 day = (24 × 60 × 60) s = 86400 s

α = `1.2 xx 10^-5"/"^circC, Deltatheta = 20 - 15 = 50^circC`

∴ ΔT = `(86400 xx 1.2 xx 10^-5 xx 5)/2 = 2.6` s