A stone of mass 1kg tied to a light inextensible sstring of length `L=10m` is whirling in a circular path of radius `L` in vertical plane. If the ratio of the maximum tension in the string to the minimmum tension in the string is 4 and if `g` is taken to be `10ms^(-2)` , the speed of the stone at the highest point of the circle is.

Options

A. 20 metre per sec
B. `10^(sqrt3)` metre per sec
C. `5(sqrt3)` metre per sec
D. 10 metre per sec

Answer

D

Explanation

In case of circular motion
motion in a vertical plane, the tension is maximum at the lowest point A but minimum at the highest point C.
For circular motion at lowest point A.

`T_(A)-Mg=(MV_(A)^(2))/(L)`
`"or "T_(A)=Mg+(MV_(A)^(2))/(L)=T_("max")" .....(i)"`
For circular motion at the highest point C :
`T_(C)+Mg=(MV_(C)^(2))/(L)`
`"or "T_(C)=(MV_(C)^(2))/(L)-Mg=T_("min")`
`((MV_(A)^(2))/(L)+Mg)/((MV_(C)^(2))/(L)-Mg)=(T_("max"))/(T_("min"))=(4)/(1)`
`(V_(A)^(2)+gL)/(V_(C)^(2)-gL)=(4)/(1)`
`"But, "V_(A)^(2)=V_(C)^(2)+2g(2L)=V_(C)^(2)+4gL`
`(V_(C)^(2)+5gL)/(V_(C)^(2)-gL)=(4)/(1) or 3V_(C)^(2)=9gL`
`"or "V_(C)^(2)=3gL=3xx10xx(10)/(3)xx100`
`=10m//s`.