Consider the situation as shown in the figure. Find `(T_(min))/(T_(max))`.

Explanation

`u=sqrt(gL), ultsqrt(2gL)`, the ball will oscillate like a simple pendulum of amplitude`lt90^(@)`.
`v^(2)=u^(2)-2gh`
`0=gL-2gL(1-cos theta)impliescostheta=(1)/(2)impliestheta=60^(@)`
`T_(max)-mg=(m u^(2))/(L)=(m)/(L)xxgLimpliesT_(max)=2mg`
`T_(min)-mg cos theta=(mv^92))/(L)impliesT_(min)-mg cos 60^(@)=0`
implies `T_(min)=(mg)/(2)`
`(T_(min))/(T_(max)0=(1)/(4)`