The wires `A` and `B` shown in Fig. 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 `mg//3`, one of the wires breaks. Then

Options

A. A breaks if `r_(A) = r_(B)`
B. A breaks if `r_(A) lt 2 r_(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

A, B, C

Explanation

Stress in wire `A =(((mg+mg)/(3)))/(pi r_(A)^(2))=(4 mg)/(3 pir_(A)^(2))`
Stress in wire `B = (((mg)/(3)))/(pi r_(B)^(2))=(mg)/(3 pi r_(B)^(2))`
Wire A will break if stress in A is more than B
`(4mg)/(3 pir_(A)^(2))gt (mg)/(3 pi r_(B)^(2))rArr 2r_(B) gt r_(A)`.