when a force F1 is applied on a wire its length is L1 & when a force F2 on the same wire its final length is L2. What is the initial length of the wire when no force is applied on it?

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Solution

Dear Student,

we know that force on the wire is proportional to the change in its length. i.e.,

F = kx. Therefore,

$l e t i n i t i a l l e n g t h b e' L', t h e n c h a n g e i n l e n g t h w h e n f o r c e s F_{1}, F_{2} a r e a p p l i e d w i l l b e (L - L_{1}) a n d (L - L_{2}) r e s p e c t i v e l y, S o, F_{1} = k (L - L_{1}) (1) a n d, F_{2} = k (L - L_{2}) (2) (1) / (2) g i v e s : \frac{F_{1}}{F_{2}} = \frac{k (L - L_{1})}{k (L - L_{2})} = \frac{(L - L_{1})}{(L - L_{2})} S o l v i n g i t : L = \frac{(F_{1} L_{2} - F_{2} L_{1})}{(F_{1} - F_{2})}$

Regards,
Manoj Singh.

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