Mechanical Properties of Solids

JEE Main level, numerical answer, medium

23 of 118

Question 23 of 118

An elastic spring under tension of 3 N3 \mathrm{~N} has a length aa. Its length is bb under tension 2 N2 \mathrm{~N}. For its length (3a−2b)(3 a-2 b), the value of tension will be______N\mathrm{N}.

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Answer: 5

3=K(a−ℓ)2=K(b−ℓ)T=K(3a−2 b−ℓ)T=K(3(a−ℓ)−2( b−ℓ)=K[3(3 K)−2(2 K)]=9−4=5 N\begin{aligned} & 3=\mathrm{K}(\mathrm{a}-\ell) \\ & 2=\mathrm{K}(\mathrm{b}-\ell) \\ & \mathrm{T}=\mathrm{K}(3 \mathrm{a}-2 \mathrm{~b}-\ell) \\ & \mathrm{T}=\mathrm{K}(3(\mathrm{a}-\ell)-2(\mathrm{~b}-\ell) \\ & =\mathrm{K}\left[3\left(\frac{3}{\mathrm{~K}}\right)-2\left(\frac{2}{\mathrm{~K}}\right)\right] \\ & =9-4 \\ & =5 \mathrm{~N}\end{aligned}

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