Laws of Motion

JEE Main level, numerical answer, medium

111 of 210

Question 111 of 210

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.

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Answer: 1

T=K(ℓ−ℓ0)⇒5=K(1.4−ℓ0)⇒7=K(1.56−ℓ0)⇒51.4−ℓ0=71.56−ℓ0∴ℓ0=1 m\begin{aligned} & \mathrm{T}=\mathrm{K}\left(\ell-\ell_0\right) \\ & \Rightarrow 5=\mathrm{K}\left(1.4-\ell_0\right) \\ & \Rightarrow 7=\mathrm{K}\left(1.56-\ell_0\right) \\ & \Rightarrow \frac{5}{1.4-\ell_0}=\frac{7}{1.56-\ell_0} \\ & \therefore \ell_0=1 \mathrm{~m}\end{aligned}

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