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Question

The length of an elastic string is $$a$$ metre when the longitudinal tension is $$4$$N and $$b$$ metre when the longitudinal tension is $$5$$N. The length of the string in metre when longitudinal tension is $$ 9 $$N is :


A
ab
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B
5b4a
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C
2b14a
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D
4a3b
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Solution

The correct option is B $$5b-4a$$
Let L is the original length of the wire and k is force constant of wire.
Final length $$=$$ initial length $$+$$ elongation
$$L'=L+\displaystyle\frac{F}{k}$$
For first condition $$a=L+\displaystyle\frac{4}{k}$$     .....$$(i)$$
For second condition $$b=\displaystyle L+\frac{5}{k}$$   ......$$(ii)$$
By solving Eqs. $$(i)$$ and $$(ii)$$, we get
$$L=5a-4b$$ and $$k=\displaystyle\frac{1}{b-a}$$
Now, when the longitudinal tension is $$9N$$. length of the string.
$$=L+\displaystyle\frac{9}{k}=5a-4b+9(b-a)$$
$$=5b-4a$$

Physics

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