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. `P` breaks, if `r_(p) = r_(Q) `
B. `P` breaks, if `r_(p)lt 2r_(Q) `
C. Either `P` or `Q` may break , if `r_(p) = 2r_(Q)`
D. To predict , which wire will break, the lengths of `P` and `Q` may break, the lengths of `p` and `Q` must be known

Answer

A, B, C

Explanation

When , `T_(Q) = (mg)/(3)`
and `T_(p) = mg+ (mg)/(3) = (4mg)/(3)`
Stress, ` sigma = (T)/(pir^(2))` ` sigma_(P)/(sigma_(Q)) = (T_(P))/(T_(Q)). ((r_(Q))/(r_(P)))^(2)`
If `r_(P) =r_(Q) , sigma_(P) = 4 sigma_(Q)`, then P breaks.
If` r_(P) lt 2r_(Q) , sigma _(P)gt sigma_(Q)`, then P breaks .
If `r_(P) = 2r_(Q) , sigma _(A) = sigma _(B) `, then either P or `Q` may break.