When the string of a conical pendulum makes an angle of `45^(@)` with the vertical , its time is `T_(1)` when the string makes an angle of `60^(@)` with the vertical , its time period is `T_(2)` then `T_(1)^(2) // T_(2)^(2)`is

Options

A. `2`
B. `sqrt(2)`
C. `0.5`
D. none of these

Answer

b

Explanation

In conical pendulum

`T cos theta = mg =` constant
`T_(1) cos theta_(1) = T_(2) cos theta_(2)`
`(T_(1))/(T_(2)) = (cos theta _(1))/(cos theta_(2)) =(cos 60^(@))/(cos 45^(@))`
`= (1//2)/(1//sqrt(2)) = (1)/(sqrt(2))`
`(T_(1)/(T_(2)^(2))) = (1)/(2)`