The length of a rubber cord is $l_{1}$ when the tension is $4 N$ and $l_{2} m$ when the tension is $6 N$ . The length when the tension is $9 N$ , is:

(2.5 l_{2} - 1.5 l_{1}) m

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(6 l_{2} - 1.5 l_{1}) m

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(3 l_{2} - 2 l_{1}) m

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(3.5 l_{2} - 2.5 l_{1}) m

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Solution

The correct option is A $(2.5 l_{2} - 1.5 l_{1}) m$
Let the original unstretched length be $l$ .
$∴ Y = \frac{T}{A} \frac{l}{Δ l}$
Now $Y = \frac{4}{A} \frac{l}{(l_{1} - l)} = \frac{6}{A} \frac{l}{(l_{2} - l)} = \frac{9}{A} \frac{l}{(l_{3} - l)}$

$∴ 4 (l_{3} - l) = 9 (l_{1} - l) o r 4 l_{3} + 5 l = 9 l_{1} . . . (i)$

Again $6 (l_{3} - l) = 9 (l_{2} - l) o r 2 l_{3} + l = 3 l_{2} . . . (i i)$

To obtain $l_{3}$ , solve (i) and (ii) simulatneously
$∴ l_{3} = (2.5 l_{2} - 1.5 l_{1}) m$

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