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  4. 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

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Q. 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

MHT CETMHT CET 2009

Solution:

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