A uniform metal rod is used as a bar pendulum. If the room temperature rises by `10^(@)C`, and the coefficient of linear expansion of the metal of the rod is `2 xx 10^(-6) per^(@)C`, the period of the pendulum will have percentage increase of

Options

A. `-2xx10^-3`
B. `-1xx10^-3`
C. `2xx10^-3`
D. `1xx10^-3`

Answer

D

Explanation

We know that `T=2pisqrt((L)/(g))`
`:. DeltaT=(2pi)/(2)((1)/(Lg))^(1//2)DeltaL`
or `(DeltaT)/(T)=(DeltaL)/(2L)=(1)/(2)alphaDeltatheta=(2xx10^-6xx10)/(2)=10^(-5)`
`:. (DeltaT)/(T)xx100=1xx10^-5xx100=10^-3%`