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 ........
JEE MAIN 2023, Medium
Download our app for free and get started
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 $120= K \left(\ell_2-\ell_0\right)$
$\frac{1}{2} \Rightarrow \frac{5}{6}=\frac{\ell_1-\ell_0}{\ell_2-\ell_0}$
$5 \ell_2-5 \ell_0=6 \ell_1-6 \ell_0$
$\ell_0=6 \ell_1-5 \ell_2$
$\ell_0=6 \ell_1-5\left(\frac{11 \ell_1}{10}\right)$
$\ell_0=6 \ell_1-\frac{11 \ell_1}{2}$
$\ell_0=\frac{\ell_1}{2}$
$\therefore x=2$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $F$, its length increases by $5\,cm$. Another wire of the same material of length $4 L$ and radius $4\,r$ is pulled by a force $4\,F$ under same conditions. The increase in length of this wire is $....cm$.View Solution
- 2View SolutionThe elastic limit for a gas
- 3View SolutionThe load versus elongation graph for four wires of same length and the same material is shown in figure. The thinnest wire is represented by line
- 4A wire can be broken by applying a load of $20\, kg$ weight. The force required to break the wire of twice the diameter is .......... $kg\, wt$View Solution
- 5View SolutionThe following four wires are made of same material. Which one will have the largest elongation when subjected to the same tension ?
- 6An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material isView Solution
- 7View SolutionThe load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line
- 8Join the relation of physical quantities in Column$-I$ to the details given in Column$-II$ appropriately :View Solution
Column $-I$ Column $-II$ $(a)$ Stress $\propto $ Strain $(i)$ $M^1\,L^{-1}\,T^{-2}$ $(b)$ Dimensional formula for compressibility $(ii)$ $M^{-1}\,L^{1}\,T^{-2}$ $(iii)$ Poisson’s ratio $(iv)$ Hooke’s law - 9A block of mass $M$ is suspended from a wire of length $L$, area of cross-section $A$ and Young's modulus $Y$. The elastic potential energy stored in the wire isView Solution
- 10View SolutionThe shear strain is possible in .............