Question

The length of a metal wire is $10$ $cm$ when the tension in it is $20$ $N$ and $12$ $cm$ when the tension is $40$ $N$. Then natural length of the wire is in $cm$.

• A. $6$
• B. $4$
• C. $8$
• D. $9$

Answer 1

The correct option is C $8$

Natural Length ${}^{\prime }{L}^{\prime }=\frac{T_2{L}_1-T_1{L}_2}{T_2-T_1}$

$T_2=40$ $N$

$L_2=12$ $cm$

$T_1=20$ $N$

$L_1=10$ $cm$

$\Rightarrow L=\frac{40\times 10-20\times 12}{40-20}$

$\Rightarrow L=8$ $cm$