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. Then,

A
A will break before B if rA=rB.
B
A will break before B if rA<2rB.
C
either A or B may break ifrA=2rB.
D
the lengths of A and B must be known to predict which wire will break.

Solution

## The correct options are A A will break before B if rA=rB. B A will break before B if rA<2rB. C either A or B may break ifrA=2rB. TB=mg3..........(1) TA=mg+mg3=4mg3  TA=4TB.......(2) Breaking stress for wire B S=TBπr2B........(3) Breaking stress of wire A S′=TAπr2A............(4) If  rA=rB Divide (3) by (4), we get S′=4S Both wire A and B made of same material. If stress developed in wire B is S for a particular load, then stress developed in wire B is 4 times of S.Therefore wire A will break first. If rA<2rB then area of A is less than area of A and we know if area is less, stress developed is more. Hence wire A will break before B. If rA=2rB and if we divide (3) by (4), we get S′=S. So we cannot predict which wire will break first.

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