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. `(4mgL)/(piD^2Y)`
B. `(4mgL)/(piD^2Ysintheta)`
C. `(4mgL)/(piD^2Ycostheta)`
D. `(4mgL)/(piD^2Ytantheta)`

Answer

C

Explanation

The situation is as shown in the figure.
Refer figure
For vertical equilibrium of stone
`Tcostheta=mg` or `T=(mg)/(costheta)` .(i)
As `Y=(T)/(A)(L)/(triangleL)` (using (i))
`triangleL=(TL)/(AY)`
`=`(mgL)/(costheta((piD^2)/(4))Y)=(4mgL)/(piD^2costheta)`