Q.
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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a
3ℓ2+4ℓ1
b
3ℓ2+2ℓ1
c
5ℓ2−4ℓ1
d
3ℓ2−2ℓ1
answer is C.
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Detailed Solution
Let 'ℓ' be the original length and ℓ3 be the length of the wire when the tension is 9N. We know e∝F ⇒ (ℓ1−ℓ)∝4.....(1),(ℓ2−ℓ)∝5.....(2)(ℓ2−ℓ)∝9.......(3)From 'l'(1)&(2)ℓ1−ℓℓ2−ℓ=45⇒5ℓ1−5ℓ=4ℓ2−4ℓℓ=5ℓ1−4ℓ2............(4)From (1)&(3)ℓ1−ℓℓ3−ℓ=49 Put is above equation and we get ℓ3=5ℓ2−4ℓ1
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