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Physics-

General

Easy

Question

The length of a rubber cord is $l subscript 1 blank end subscript$ metre when the tension is 4 N and $l subscript 2 blank end subscript$ metre when the tension is 6N. The length when the tension is 9 N, is

${(2.5 l}_{2} - 1.5 l_{1}) m$
${(6 l}_{2} - 1.5 l_{1}) m$
${(3 l}_{2} - 2 l_{1}) m$
${(3.5 l}_{1} - 2.5 l_{1}) m$

The correct answer is: $left parenthesis 2.5 l subscript 2 end subscript minus 1.5 l subscript 1 blank end subscript right parenthesis m$

Let the original unstretched length be $l.$
$Y equals fraction numerator S t r e s s over denominator S t r a i n end fraction equals fraction numerator T divided by A over denominator increment l divided by l end fraction equals fraction numerator T over denominator A end fraction cross times fraction numerator l over denominator increment l end fraction$
Now, $Y equals fraction numerator 4 over denominator A end fraction fraction numerator l over denominator open parentheses l subscript 1 end subscript minus l close parentheses end fraction equals fraction numerator 6 over denominator A end fraction fraction numerator l over denominator open parentheses l subscript 2 end subscript minus l close parentheses end fraction equals fraction numerator 9 over denominator A end fraction fraction numerator l over denominator open parentheses l subscript 3 end subscript minus l close parentheses end fraction$
$therefore blank 4 open parentheses l subscript 3 end subscript minus l close parentheses equals 9 open parentheses l subscript 1 end subscript minus l close parentheses$
$⟹ 4 l subscript 3 end subscript plus 5 l equals 9 l subscript 1 end subscript blank left parenthesis i right parenthesis$
Again, $6 open parentheses l subscript 3 end subscript minus l close parentheses equals 9 open parentheses l subscript 2 end subscript minus l close parentheses$
⟹ $blank 2 l subscript 3 end subscript plus l equals 3 l subscript 2 end subscript blank left parenthesis i i right parenthesis$
Solving Eqs. (i) and (ii), we obtain
$l subscript 3 end subscript equals left parenthesis 2.5 l subscript 2 end subscript minus 1.5 l subscript 1 end subscript right parenthesis$

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