If the length of a string is P when the tensi | vedclass

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(D) Let $L$ be the original length of the string and $k$ be the force constant of the string.The final length is given by: $	ext{Final length} = 	ex

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$4P - 3Q$

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(D) Let $L$ be the original length of the string and $k$ be the force constant of the string.The final length is given by: $	ext{Final length} = 	ext{Original length} + 	ext{Elongation}$.Using Hooke's Law,$	ext{Elongation} = \frac{F}{k}$.Thus,$L' = L + \frac{F}{k}$.For the first condition: $P = L + \frac{6}{k} \quad ...(i)$For the second condition: $Q = L + \frac{8}{k} \quad ...(ii)$To eliminate $k$,multiply equation $(i)$ by $4$ and equation $(ii)$ by $3$:$4P = 4L + \frac{24}{k} \quad ...(iii)$$3Q = 3L + \frac{24}{k} \quad ...(iv)$Subtracting equation $(iv)$ from equation $(iii)$:$4P - 3Q = (4L - 3L) + (\frac{24}{k} - \frac{24}{k})$$4P - 3Q = L$Therefore,the original length of the string is $4P - 3Q$.

If the length of a string is $P$ when the tension in it is $6 \ N$ and its length is $Q$ when the tension in it is $8 \ N$,then the original length of the string is

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