A pendulum clock consists of an iron rod connected to a small, heavy bob. If it is designed to keep correct time at 20∘C, then how fast or slow will it go in 24 hours at 40∘C ? Co-efficient of linear expansion of iron = 1.2×10−6/∘C.
The correct option is A 1.04 s, slow
Time period in a pendulum is given as T=2π√lg
When temperature is increased by Δθ new length is l=l0(1+αΔθ)
As T is proportional to √l
So new Time period T=T0√(1+αΔθ)
As αΔθ <<1 applying Binomial theorem,
For calculating variation of time for 24 hrs⇒T0=86400 s
As there is increase in length due to rise of temperature, time period of pendulum increases and clock runs slow.