A simple pendulum made of bob of mass `m` and a metallic wire of negligible mass has time period `2 s` at `T = 0^(@)C`. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope `S`. If the coefficient of linear expansion of metal is `alpha` then value of `S` is :

Options

A. `alpha`
B. `(alpha)/(2)`
C. `2alpha`
D. `(1)/(alpha)`

Answer

A

Explanation

`t_(0) = 2 = 2pisqrt((l_(0))/(g))`
`t = 2pisqrt((l_(0)(1 + alphaT))/(g)) = 2(1 + alphaT)^(1//2) = 2 + alphaT`
`t - t_(0) = alphaT rArr Deltat= alphaT`