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
B
5b4a
C
2b14a
D
4a3b

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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