- Home
- Standard 11
- Physics
8.Mechanical Properties of Solids
medium
The length of wire becomes $l_1$ and $l_2$ when $100\,N$ and $120\,N$ tensions are applied respectively. If $10l_2=11l_1$, the natural length of wire will be $\frac{1}{x} l_1$. Here the value of $x$ is ........
A
$8$
B
$2$
C
$6$
D
$4$
(JEE MAIN-2023)
Solution
Let the original length be ' $\ell_0$ '
When $T _1=100\,N$, Extension $=\ell_1-\ell_0$
When $T _2=120\,N$, Extension $=\ell_2-\ell_0$
Then $100= K \left(\ell_1-\ell_0\right)$
And $120= K \left(\ell_2-\ell_0\right)$
$\frac{1}{2} \Rightarrow \frac{5}{6}=\frac{\ell_1-\ell_0}{\ell_2-\ell_0}$
$5 \ell_2-5 \ell_0=6 \ell_1-6 \ell_0$
$\ell_0=6 \ell_1-5 \ell_2$
$\ell_0=6 \ell_1-5\left(\frac{11 \ell_1}{10}\right)$
$\ell_0=6 \ell_1-\frac{11 \ell_1}{2}$
$\ell_0=\frac{\ell_1}{2}$
$\therefore x=2$
Standard 11
Physics
