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. `2 alpha `
D. `1/ alpha`

Answer

A

Explanation

`t_0 2 = 2pi sqrt( (l_0)/(g) )`
` t = 2pi sqrt( (l_0 (1+alphaT))/(g) ) = (2pi sqrt( (l_0)/(g) ) ) sqrt((1 + alphaT))`
` t_0 (1+ alpha T)^(1/2) rArr t_0 (1+ 1/2 alpha Tt …..)`
` t - t_0 = t_0 alpha T// 2`
`Delta t = alpha T`