A wire of length $L$ is hanging from a fixed support. The length changes to $L _{1}$ and $L _{2}$ when masses $1 \,kg$ and $2 \,kg$ are suspended respectively from its free end. Then the value of $L$ is equal to ..................
JEE MAIN 2022, Diffcult
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By Hooke's Law
so $F \alpha \Delta L$
$\frac{ F _{1}}{ F _{2}}=\frac{\Delta L _{1}}{\Delta L _{2}}$
$\frac{10}{20}=\frac{\left(L_{1}-L\right)}{\left(L_{2}-L\right)}$
$L =2 L _{1}- L _{2}$
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