A particle `A` of mass `m` is attached to a vertical axis by two stings `PA` and `QA` of lengths `3L` and `4L` , respectively. `PQ=5L`. A rotates around the axis with an angular speed `omega`. The tension in the two strings are `T_(1)` and `T_(2)`.

(i) `T_(1)=T_(2)`
(ii) `3T_(1)-4T_(2)=5mg`
(iii) `4T_(1)+3T_(2)=12momega^(2)L`

Options

A. `(i)`only
B. `(i),(ii)`
C. `(i),(iii)`
D. `(ii),(iii)`

Answer

D

Explanation

`/_PAQ=90^(@)`
`Sinalpha=(4)/(5),cosalpha=(3)/(5)`
`sinbeta=(3)/(5),cosbeta=(4)/(5)`
`r=3Lsinalpha=(12L)/(5)`
`T_(1)cosalpha=T_(2)cosbeta+mg`
`T_(1)xx(3)/(5)=T_(2)xx(4)/(5)+mg`
`3T_(1)-4T_(2)=5mg`
`T_(1)xx(4)/(5)+T_(2)xx(3)/(5)=momega^(2)((12L)/(5))`
`4T_(1)+3T_(2)=12momega^(2)L`