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An elastic spring under tension of $3 \mathrm{~N}$ has a length $a$. Its length is $b$ under tension $2 \mathrm{~N}$. For its length $(3 a-2 b)$, the value of tension will be______$\mathrm{N}$.
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The correct answer is:
5
$\begin{aligned} & 3=\mathrm{K}(\mathrm{a}-\ell) \\ & 2=\mathrm{K}(\mathrm{b}-\ell) \\ & \mathrm{T}=\mathrm{K}(3 \mathrm{a}-2 \mathrm{~b}-\ell) \\ & \mathrm{T}=\mathrm{K}(3(\mathrm{a}-\ell)-2(\mathrm{~b}-\ell) \\ & =\mathrm{K}\left[3\left(\frac{3}{\mathrm{~K}}\right)-2\left(\frac{2}{\mathrm{~K}}\right)\right] \\ & =9-4 \\ & =5 \mathrm{~N}\end{aligned}$
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