Mechanical Properties of Solids

JEE Main level, single correct, medium

69 of 118

Question 69 of 118

Young's moduli of two wires AA and BB are in the ratio 7:47:4 . Wire AA is 2m2m long and has radius R.R. Wire BB is 1.5m1.5m long and has radius 2mm.2mm. If the two wires stretch by the same length for a given load, the value of RR is close to:

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Answer: (D) 1.7mm1.7mm

Strain =∆l/l=∆l/l
Stress =F/A=F/A
Young’s modulus =StressStrain=F/A(∆l/l)=FA(l∆l)=\dfrac{Stress}{Strain}=\dfrac{F/A}{\left(∆l/l\right)}=\dfrac{F}{A}\left(\dfrac{l}{∆l}\right)
YAYB=(lAAA)(ABlB)=74\dfrac{{Y}_{A}}{{Y}_{B}}=\left(\dfrac{{l}_{A}}{{A}_{A}}\right)\left(\dfrac{{A}_{B}}{{l}_{B}}\right)=\dfrac{7}{4}
(2πrA2)(πrB21.5)=74\left(\dfrac{2}{\pi {r}_{A}^{2}}\right)\left(\dfrac{\pi {r}_{B}^{2}}{1.5}\right)=\dfrac{7}{4}
rA2=21.5×7×(2mm)2{r}_{A}^{2}=\dfrac{2}{1.5\times 7}\times {\left(2mm\right)}^{2}
rA=1.7mm{r}_{A}=1.7mm

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