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

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 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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