A stone of mass `m` 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 6 with the vertical. If Young's modulus of the wire is `Y`, Then the increase in the length of the wire is

Options

A. `(mg l cos theta)/(AY)`
B. `(mg l )/(AY cos theta)`
C. `(mg lY )/(A cos theta)`
D. `(mg lA )/(Y cos theta)`

Answer

B

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)`