a ball of mass `240g` is attached to the verticle rod by means of two strings. When the ball rotates about the axis of rod, the strings are extended as shown in the figure.
(a) find the angular speed of the ball if tension in lower string is `16N`.
(b) What is tension in the upper string?

Explanation

`uarr:T_(1) cos theta-T_(2)costheta=mg` …..`(i)`
`larr:T_(1)sin theta+T-(2)sin theta=momega^(2)r` …..`(ii)`
`sin theta=(r )/(L)` ….`(iii)`
From `(i)`, we have
`(T_(1)-T_(2))=(mg)/(cos theta)=((0.24xx10)/(0.9)/(1.5))=4` …..`(iv)`
from `(ii)` and `(ii)`, we get
`(T_(1)+T_(2)) sin theta=momega^(2) L sin theta`
`T_(1)+T_(2)=m omega^(2)L=0.24 omega^(2)xx1.5=0.36 omega^(2)` ....`(v)`
`T_(1)-T_(2)=4impliesT_(1)-16=4impliesT_(1)=20N`
`T_(1)+T_(2)=0.36 omega^(2)implies20+16=0.36omega^(2)`
`implies omega^(2)=100impliesomega=10 rad//s`