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).

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

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.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity