Length of an elastic string is a metre when longitudinal tension is 4, N and b metre when longitudin

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8.Mechanical Properties of Solids

hard

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 the longitudinal tension is $9\, N$ is

A

$a - b$

B

$5b - 4a$

C

$2b - \frac{1}{4}a$

D

$4a - 3b$

Solution

(b) 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 $(i)$ and $(ii)$ equation we get

$L = 5a – 4b$ and $K = \frac{1}{{b – a}}$

Now when the longitudinal tension is $9N,$

length of the string $=$ $L + \frac{9}{K}$= $5a – 4b + 9(b – a)$$x = 5b – 4a$.

Standard 11

Physics

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