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. for `r_(1) = r_(2),2` should be broken before 1.
B. for `r_(1)` less than `2r_(2),2` should be broken before `1`
C. data is indufiicent
D. for `r_(1) = 2r_(2)`, any of the two may break

Answer

D

Explanation

Stress for wire `1, S_(1) = (4Mg)/(3 xx pi r_(1)^(2))` and
stress for wire `2, S_(2) = (Mg)/(3 xx pi r_(2)^(2))`
for `r_(1) = r_(2), S_(1) = 4S_(2)`
`therefore` any of the two wires may break because stress is same