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  4. Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is (24/π) × 102 Nm -2. What is the minimum radius of the wire? (. Take .g =10 ms -2)

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Q. Two blocks of masses $3\, kg$ and $5 \,kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2} \,Nm ^{-2}$. What is the minimum radius of the wire?
$\left(\right.$ Take $\left.g =10 \,ms ^{-2}\right)$Physics Question Image

JEE MainJEE Main 2021Mechanical Properties of Solids

Solution:

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$T =\frac{2 m _{1} m _{2} g }{ m _{1}+ m _{2}}$
$=\frac{2 \times 3 \times 5 \times 10}{8} $
$=\frac{75}{2}$
Stress $=\frac{T}{A}$
$\frac{24}{\pi} \times 10^{2}=\frac{75}{2 \times \pi R^{2}}$
$R^{2}=\frac{75}{2 \times 24 \times 100}=\frac{3}{8 \times 24}$
$\Rightarrow R=0.125 \,m$
$R=12.5\, cm$