A steel wire $1.5\;m$ long and radius $1\;mm$ is attached with a load of $3 \;Kg$ at one end and the other end of he wire is fixed. It is wirled in a vertical circle with frequency $2\;Hz$. find the elongation of the wire when the weight is at the lowest position. $[Y=2 \times 10^{11} N/m^2 \quad g=10m/s^2]$

Question

$$\begin {array} {1 1} (a)\;1.77 \times 10^{-3}\;m \\ (b)\;7.17 \times 10^{-3}\;m \\ (c)\;3.17 \times 10^{-7}\;m \\ (d)\;1.37 \times 10^{-7}\;m \end {array}$$