A stone of mass (m) is attached to one end of a small wire of length `(l)` and cross-sectional area (A) suspended vertically. The stone is now rotated in horizontal plane such that the wire makes an angle .`theta`. with vertical. Find the increase in length of wire if its Young.s modulus is Y.

Explanation

From fig, `T cos theta = mg rArr T = (mg)/(cos theta)`
`T sin theta = m R omega^2`
` e = (Fl)/(AY) = (Tl)/(AY)`
` e = (mgl)/(AY cos theta)`
If `theta` was not given but R ,w and m was given then in such case
`T^2 cos^2 theta = T^2 sin^2 theta = (mg)^2 + (mR w^2)^2`
` T = sqrt((mg)^2 + (mR w^2)^2) ` and use `e = (Tl)/(Ay)`