A bob of 1 kg wt is suspended by a rubber cord 2m long and of cross section `0.5 cm^2` it is made to descrbie a horizontal circle of radius 50cm, 4 times a second. Find the extension of the cord, Young's modulus of rubber is `5xx10^8 N//m^2`

Explanation

`T cos theta = mg` ..(i)
and `T sin theta = mr omega^(2) = mr 4 pi^(2)v^(2)`..(ii)
Squaring and adding (i) and (ii) , we get
`T = sqrt((mg)^(2)+(mr 4 pi^(2)v^(2))^(2))`
`= sqrt((1 xx 9.8)^(2) +[1xx0.5xx4xx(22//7)^(2)xx4^(2)]^(2))`
`=316N`
Now , `Delta l = (Tl)/(AY) = (316 xx 2)/((0.5 xx 10^(-4)) xx (5 xx 10^(8)))`
`= 0.02528 m = 2.528cm`.