Mechanical Properties of Solids

JEE Main level, single correct, medium

31 of 118

Question 31 of 118

A wire of length LL and radius rr is clamped rigidly at one end. When the other end of the wire is pulled by a forceff, its length increases by ll. Another wire of same material of length 2L2L and radius 2r2r is pulled by a force 2f2f. Then the increase in its length will be:

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Answer: (D) ll

Young's modulus is same for both the wires since the material is same.
For the first wire,
Y=fLπr2l...(i)Y=\dfrac{fL}{\pi {r}^{2}l}...(i)
For the second wire,
Y=2f(2L)4πr2l′...(ii)Y=\dfrac{2f(2L)}{4\pi {r}^{2}l'}...(ii)
Dividing (i) by (ii)
fLπr2l×4πr2l′4fL=1⇒l′=l\dfrac{fL}{\pi {r}^{2}l}\times \dfrac{4\pi {r}^{2}l'}{4fL}=1 \Rightarrow l'=l

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