A plumb bob is suspended by a light rod inside a car moving in a circular horizontal track of radius `(6sqrt3)/5` m . The angle made by the rod with the vertical is found out to be` 60^@`. Then, the car moves with a constant speed of ___ m/s.`(g = 10 m//s^2)`

Answer

6

Explanation

T sin `theta` = `(mv^2)/R`
T cos `theta` = mg
`therefore tan theta = (v^2)/(Rg) `
`therefore v^2 = tan theta xx R x g`
`therefore v^2 = tan 60 ^@ xx (6sqrt3)/5 xx 10`
`therefore v^2 = sqrt3 xx( 6sqrt3)/5 xx 10`
`therefore v^2 = 36`
`therefore` v = 6 m/s