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Two light wires P and Q shown in the figure are made of the same material and have radii $r_{P}$ and $r_{Q}$ , respectively. The block between them has a mass m. When the force $F = \frac{m g}{3} i s a p p l i e d,$ , one of the wires breaks. Choose the correct option(s).

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P breaks, if $r_{P} = r_{Q}$

Either P or Q may break, if $r_{P} = 2 r_{Q}$

To predict, which wire will break, the lengths of P and Q must be known

P breaks, if $r_{P} < 2 r_{Q}$

answer is A, B, C.

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Detailed Solution

When, $T_{Q} = \frac{m g}{3} a n d T_{P} = m g + \frac{m g}{3} = \frac{4 m g}{3}$

Stress,

$Stress, σ = \frac{T}{π r^{2}} \Rightarrow \frac{σ_{P}}{σ_{Q}} = \frac{T_{p}}{T_{Q}} \cdot {(\frac{r_{Q}}{r_{P}})}^{2}$

If $r_{P} = r_{Q}, σ_{P} = 4 σ_{Q}$ , then P breaks.

If $r_{P} < 2 r_{Q}, σ_{P} > σ_{Q}$ , then P breaks.

If $r_{P} = 2 r_{Q}, σ_{A} = σ_{B}$ , then either P or Q may break.

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