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. `Tcos 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)+(mRw^(2))^(2)`
`T=sqrt((mg)^(2)+(mRw^(2))^(2)) " and use e"=(Tl)/(Ay)`