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Two light wires A and B shown in the figure are made of the same material and have radii rA and rB respectively. The block between them has a mass m. When the force F is mg3 one of the wires breaks.


  1. A breaks if rA<rB

  2. A breaks if rA=rB

  3. Either A or B may break if rA=2rB

  4. The lengths of A and B must be known to predict which wire will break


Solution

The correct option is C

Either A or B may break if rA=2rB


Stress on wire A,

σA=FAπr2A=mg+mg3πr2A

=4mg3πr2A

Stress on wire B,

σB=FBπr2B=mg3πr2B

=mg3πr2B

If rArB, σA>σB and A will break. Therefore options (a) and (b) are correct. If rA=2rB, then σA=σB. Therefore either A or B may break.

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