The maximum and minimum tension in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio `5:3` then its velocity is

Options

A. `sqrt(98)ms^(-1)`
B. `7ms^(-1)`
C. `sqrt(490)ms^(-1)`
D. `sqrt(4.9)ms^(-1)`

Answer

A

Explanation

Minimum tension , `T_1=x-mg" "...(i)`
`maximum tension , T_2=x+mg" "....(ii)`
`and " "(mv^2)/(r)=x`
On dividing Eq . (i) by Eq.(ii), we get
`T_1/T_2=(x-mg)/(x+mg)" "(becausegiven T_1/T_2=3/5)`
`therefore" "3/5=(x-mg)/(x+mg)`
`or 3x+3mg=5x-5mg`
`or x=4mg " "i.e (mv^2)/(r)=4mg`
`therefore " "v^2=4rg " "or" "v=sqrt(4rg)`
`or " "v =sqrt(4xx2.5xx9.8)or" "v=sqrt(98)ms^(-1)`