Question

A stone of mass `m` tied to a light inextensible sting of length `L(=(10)/(3)m)` is whirling in a circular path of radius `L` in a verticle plane. If the ratio of the maximum to the minimum tension is four, find the speed of the stone at the highest point of the circle.

Answer 1

`v^(2)=u^(2)-2gxx2L=u^(2)-4gLimpliesu^(2)=v^(2)+4gL`
`T_(1)-mg=(m u^(2))/(L)impliesT-(1)=mg+(m u^(2))/(L)=T_(max)`
`T_(2)+mg=(mv^(2))/(L)impliesT_(2)=(mv^(2))/(L)-mg=T_(min)`
`(T_(max))/(T_(max))=(mg+(mu^(2))/(L))/((mv^(2))/(L)-mg)=(gL+u^(2))/(v^(2)-gL)`
`=(gL+v^(2)+4gL)/(v^(2)-gL)=4`
`v^(2)+5gL=4v^(2)-4gL`
`3v^(2)=9gLimpliesv=sqrt(3gL)=sqrt(3xx10xx(10)/(3))=10m//s`
Speed at the highest point`=10m//s`