Two wires Ac an Bc are tied at C of small sphere of mass 5 kg Which reolves at ta constant speed v in the horzontal circle of radius of `1.6 ` m. The minimum value of v is

Options

A. `3.01 m//s`
B. `4.01 m//s`
C. `8.2 m//s`
D. `3.96 m//s`

Explanation

(d) From the figure

`T_(1)cos30^(@)+T_(2)cos45^(@)=mg`
and `T_(1)sin30^(@)+T_(2) sin45^(@)=(mv^(2))/(r)`
From Eq. (i) and Eq. (ii) we get `T_(1)=(mg-(mv^(2))/(r))/((sqrt((3)-1)/2))`
But, `" " T_(1)-geo`
`T_(1)=(mg-(mv^(2))/(r))/((sqrt((3)-1)/2))ge0`
`mgge(mv^(2))/(r)rArrvlesqrt(rg)`
`v_(max)=(r)/sqrt(rg)=sqrt(1.6xx9.8)=3.96 m//s`