The length of a rubber cord is ℓ$$1$$ metres when the tension in it is $$4N$$ and ℓ$$2$$ metres when the tension is $$5N$$. Then the length in meters when the tension is $$9N$$ is

Question

The length of a rubber cord is ℓ$$1$$      metres when the  tension in it is $$4N$$ and ℓ$$2$$      metres when the  tension is $$5N$$. Then the length in meters when the tension is $$9N$$ is

Infinity Learn · Accepted Answer

Let 'ℓ'  be the original length and ℓ$$3$$  be the length of the wire when the tension is $$9N$$. We know e∝F ⇒ $$($$ℓ$$1$$−ℓ$$)$$∝$$4$$.....(1),$$($$ℓ$$2$$−ℓ$$)$$∝$$5$$.....(2)($$ℓ$$2$$−ℓ$$)∝$$9$$.......(3)From$$ 'l'$$(1)&(2)ℓ$$1$$−ℓℓ$$2$$−ℓ$$=45$$⇒$$5$$ℓ$$1$$−$$5$$ℓ$$=4$$ℓ$$2$$−$$4$$ℓℓ$$=5$$ℓ$$1$$−$$4$$ℓ$$2$$............(4)From$$ $$(1)&(3)ℓ$$1$$−ℓℓ$$3$$−ℓ$$=49$$    Put  is above equation and we get ℓ$$3=5$$ℓ$$2$$−$$4$$ℓ$$1$$

The length of a rubber cord is $ℓ_{1}$ metres when the tension in it is 4N and $ℓ_{2}$ metres when the tension is 5N. Then the length in meters when the tension is 9N is

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The length of a rubber cord is ℓ1 metres when the tension in it is 4N and ℓ2 metres when the tension is 5N. Then the length in meters when the tension is 9N is

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The length of a rubber cord is $ℓ_{1}$ metres when the tension in it is 4N and $ℓ_{2}$ metres when the tension is 5N. Then the length in meters when the tension is 9N is