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`

Answer

2.528 cm

Explanation

Refer to

`T cos theta = mg…..(i)`
and `T sin theta = m r omega^2 = mr 4pi^2v^2…. (ii)` Squaring and adding (i) and (ii) we have
`T = sqrT((mg)^2) + (m r omega^2)2`
`= sqrt((1xx9.8)^2 + [ 1xx0.5 xx(2pi xx 4)^2]^2)`
`~~316 N`
`Now, Delta l = (T l)/(AY) = (316xx2)/(0.5xx10^(-4)xx5xx 10^8)`
= 0.02528m = 2.528 cm