Consider a stone of mass 1 kg tied to a light inextensible string and whirling in a vertical circular path. The length of the string is fount to be `10/4` m. It is also fount that theratio of the maximum to minimum tension is 3. The find the speed of the stone at the highest point of the circle in `ms^(-1)`. (Take `g=10ms^(-2)`)

Answer

`10.00`

Explanation

The ratio of maximum `(T_(L))` to the minimum tension `(T_(H))` is
`:.T_(L)=3T_(H)`
The difference between the two tensions should
be 6 mg
`:. T_(L)-T_(H)=6mg`
`:.3T_(H)-T_(H)=6mg`
`:.2T_(H)=6mg`
`:.T_(H)=3mg`
Tension at the highest pointof the circle is
`T_(H)+mg=(mv_(H)^(2))/r=(mv_(H)^(2))/L`
`3mg+mg=(mv_(H)^(2))/(10/4):.4mg=(mv_(H)^(2))/(10/4)`
`:.v_(H)^(2)=4gxx10/4`
`:.v_(H)=sqrt(10xx10)`
`:.v_(H)=10m//s`