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A stone of mass m is tied to one end of ...

A stone of mass `m` is tied to one end of a wire of length L. The diameter of the wire is D and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle θ with the vertical. If Young's modulus of the wire is `Y`, Then the increase in the length of the wire is

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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)`
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