Question

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:

• A. $\sqrt{ L _{1} L _{2}}$
• B. $\frac{ L _{1}+ L _{2}}{2}$
• C. $2 L _{1}- L _{2}$
• D. $3 L_{1}-2 L_{2}$

Answer 1

Answer: (C)

By Hooke's Law
so $F \alpha \Delta L$
$\frac{ F _{1}}{ F _{2}}=\frac{\Delta L _{1}}{\Delta L _{2}}$
$\frac{10}{20}=\frac{\left( L _{1}- L \right)}{\left( L _{2}- L \right)}$
$L =2 L _{1}- L _{2}$