Mechanical Properties of Solids

JEE Main level, single correct, medium

66 of 118

Question 66 of 118

Speed of a transverse wave on a straight wire (mass 6.0g,6.0g, length 60cm60cm and area of cross-section 1.0mm21.0m{m}^{2} is 90ms−190{ms}^{-1}. If the Young's modulus of wire is 16×1011Nm−216\times {10}^{11}N{m}^{-2}, the extension of wire over its natural length is:

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Answer: (A) 0.03mm0.03mm

v=Tμv=\sqrt{\dfrac{T}{\mu }}
⇒T=μv2\Rightarrow T=\mu {v}^{2}
⇒μv2A=Y∆ll\Rightarrow \dfrac{\mu {v}^{2}}{A}=Y\dfrac{∆l}{l}
⇒∆l=μv2lAY\Rightarrow ∆l=\dfrac{\mu {v}^{2}l}{AY}
After substituting value of μ,v,l,A\mu ,v,l,A and YY we get
∆l=0.3mm∆l=0.3mm

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