Option (a) is correct. WHY?

Dear Dear Student,
The concept of the question is that the stress produced due to its own weight should be less than the breaking stress. If it becomes greater than or equal to  breaking stress the wire will break.
And in the solution below we have just calculated stress due to its own weight. 

​​​​​​Exact answer comes out to be as shown above. 9.4 x 103 m is most close to the above answer. So we will opt this.

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