Question

The wires A and B shown in the figure are made of the same material and have radii $r_A$ and $r_B$ respectively. The block between them has a mass m. When the force F is $\frac{mg}{3}$, one of the wires breaks, then

• A. A will break before B if $r_A=r_B$
• B. A will break before B if $r_A<2r_B$
• C. Either A or B may break if $r_A=2r_B$
• D. The lengths of A and B must be known to predict which wire will break

Answer 1

Answer: (A), (B), (C)

The correct options are
A

A will break before B if $r_A=r_B$

B

A will break before B if $r_A<2r_B$

C

Either A or B may break if $r_A=2r_B$

Tension in B $=T_B=\frac{mg}{3}$
Tension in A $=T_A=T_B+mg=\frac{4mg}{3}$

$\therefore T_A=4T_B$
Stress $S=\frac{T}{\pi r^2}$
Wire breaks when S is equal to breaking stress
For $r_A=r_B,S_A=4S_B$
$\therefore$ Wire A breaks before wire B
For $r_A=2r_B,S_B=\frac{T_B}{\pi r_B^2}{S}_A=\frac{T_A}{\pi r_A^2}=\frac{4T_B}{\pi (2r_B{)}^2}\frac{T_B}{\pi r_B^2}=S_B$
As the stresses are equal, either may break.