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) m//s`
B. `7 m//s`
C. `sqrt(490) m//s`
D. `sqrt(4.9)`

Answer

A

Explanation

`T_("max") = (mv^(2))/r + mg` (at lowest point)
`T_("min") = (mv^(2))/r - mg` (at highest point)
`T_("max")/T_("min") = 5/3 rArr ((mv^(2))/r + mg)/((mv^(2))/r - mg) = 5/3`
`rArr 3mv^(2) + 3mgr = 5mv^(2) - 5mgr`
`rArr 2mv^(2) + 8mgr = 0`
`v = sqrt(4gr)`
`v = sqrt(4 xx 9.8 xx 2.5) = sqrt(98) m//s`