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Question

The 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 mg/3, one of the wires breaks. 



A
A will break before B if rA=rB
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B
A will break before B if rA=rB
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C
Either A or B may break if rA<2rB
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D

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

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Solution

The correct option is C Either A or B may break if rA<2rB

Tension in wire A=Mg+Mg3

Tension in wire B=Mg3
Stress in  A,SA=TA=43Mgπr2R
Stress in B,SB=Mgπr2R
We know that one of the wires breaks when =F=mg3
Which means if rA=rB then A should break as stress in A is greater.
We can also see that SA will be always greater unless rA>2rB which means that A will break
if rA<2rB
Similarly, when rA=2rB  stress will be the same in both wires either can break.

Physics

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