Mechanical Properties of Solids

JEE Main level, single correct, medium

58 of 118

Question 58 of 118

The length of a metal wire is ℓ1,{\ell }_{1}, when the tension in it is T1{T}_{1} and is ℓ2{\ell }_{2} when the tension is T2.{T}_{2}. The natural length of the wire is:

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Answer: (B) ℓ1T2−ℓ2T1T2−T1\dfrac{{\ell }_{1}{T}_{2}-{\ell }_{2}{T}_{1}}{{T}_{2}-{T}_{1}}

T1=k(ℓ1−ℓ0){T}_{1}=k\left({\ell }_{1}-{\ell }_{0}\right)
T2=k(ℓ2−ℓ0){T}_{2}=k\left({\ell }_{2}-{\ell }_{0}\right)
T1T2=ℓ1−ℓ0ℓ2−ℓ0\dfrac{{T}_{1}}{{T}_{2}}=\dfrac{{\ell }_{1}-{\ell }_{0}}{{\ell }_{2}-{\ell }_{0}}
T1ℓ2−T1ℓ0=T2ℓ1−T2ℓ0{T}_{1}{\ell }_{2}-{T}_{1}{\ell }_{0}={T}_{2}{\ell }_{1}-{T}_{2}{\ell }_{0}
T2ℓ1−T1ℓ2T2−T2=ℓ0\dfrac{{T}_{2}{\ell }_{1}-{T}_{1}{\ell }_{2}}{{T}_{2}-{T}_{2}}={\ell }_{0}

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