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 `theta` with the vertical. If Young's modulus of the wire is `Y`, then the increase in the length of the wire is

Options

A. `(4mgl)/(piD^(2)Y)`
B. `(4mgl)/(piD^(2)Ysin theta)`
C. `(4mgl)/(piD^(2)Y cos theta)`
D. `(4mgl)/(piD^(2)Y tan theta)`

Answer

C

Explanation

The situation is as shown in the figure. For vertical equilibrium of stone

`T cos theta = mg or T =(mg)/(cos theta)" ".....(i)`
As `Y =(T)/(A)(L)/(DeltaL) `
` therefore DeltaL = (TL)/(AY)" "("Using (i)")`
`= (mgL)/(cos theta (piD^(2)//4)Y)= (4mgl)/(piD^(2)Y cos theta)`