In the figure `PQRS` is a frictionless horizontal plane on which a particle `A` of mass `m` moves in a circle of radius `r` with an angular velocity `omega` such that `omega^(2)r=g//3` .Another particle of mass `m` is tied to `A` through an inextensible massless string. `O` is the hole through which string passes down to `B.` B can move only vertically. The tension in the string at this instant will be `:`

Options

A. `mg//3`
B. `2mg//3`
C. `mg//6`
D. none

Answer

B

Explanation

`T-m w^(2)r=ma`

`T-m((g)/(3))=ma rarr (1)`
`mg-T=ma rarr (2) T-(mg)/(3)=mg-T`
`rArr 2T=4 mg//3`
`rArr T=2mg//3 Ans. (B)`