Mechanical Properties of Solids

JEE Main level, single correct, medium

56 of 118

Question 56 of 118

Two blocks of masses 3kg3kg and 5kg5kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is 24π×102Nm−2\dfrac{24}{\pi }\times {10}^{2}N{m}^{-2}. What is the minimum radius of the wire ?
( take g=10ms−2)\left.g=10{ms}^{-2}\right)

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Answer: (D) 12.5cm12.5cm

Tension in the string =2m1m2(m1+m2)g=\dfrac{2{m}_{1}{m}_{2}}{\left({m}_{1}+{m}_{2}\right)}g
=2×3×5×108=752=\dfrac{2\times 3\times 5\times 10}{8}=\dfrac{75}{2}
Stress =TA=\dfrac{T}{A}
24π×102=752(πr2)\dfrac{24}{\pi }\times {10}^{2}=\dfrac{75}{2\left(\pi {r}^{2}\right)}
r2=7548×10−2{r}^{2}=\dfrac{75}{48}\times {10}^{-2}
r2=0.015625{r}^{2}=0.015625
r=0.125m=12.5cmr=0.125m=12.5cm

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