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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. Then,


Correct Answer
A
A will break before B if rA=rB.
Correct Answer
B
A will break before B if rA<2rB.
Correct Answer
C
either A or B may break ifrA=2rB.
Your Answer
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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