Get Answers to all your Questions

header-bg

A $1 \mathrm{~m}$ long wire is broken into two unequal parts $\mathrm{X}$ and $\mathrm{Y}$ . The $\mathrm{X}$ part of the wire is streched into another wire $\mathrm{W}$ . Length of $\mathrm{W}$ is twice the length of $\mathrm{ X}$ and the resistance of $\mathrm{W}$ is twice that of $\mathrm{Y}$ . Find the ratio of length of $\mathrm{X}$ and $\mathrm{Y}$ .
Option: 1
$1:4$

Option: 2
$1:2$

Option: 3
$4:1$

Option: 4
$2:1$

Answers (1)

best_answer

$\mathrm{R_{w}=2R_{Y}\left ( Given \right )}$

$\mathrm{\frac{R_{x}}{R_{Y}}=\frac{\ell}{1-\ell}}\rightarrow (1)$

$\mathrm{\frac{R_{W}}{R_{X}}=\frac{\left (2\ell \right )^{2}}{\left (\ell \right )^{2}}=4}\rightarrow (2)$

From the above equations

$\mathrm{R_W=4 R_X =2 R_Y }$

$\mathrm{\frac{R_X}{R_Y}=\frac{1}{2} =\frac{\ell}{1-\ell} }$

$\mathrm{1-\ell =2 \ell }$

$\mathrm{3 \ell=1 }$

$\mathrm{\ell=\frac{1}{3} }$

$\mathrm{\frac{\ell_x}{\ell_Y}=\frac{\ell}{1-\ell} =\frac{1 / 3}{2 / 3}=\frac{1}{2}}$

Hence 2 is correct option

Posted by

manish

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Trending Articles/News

anam-khan

Four Kashmiri girls defy the odds, score 99+ percentile in JEE Main 2025

anam-khan

JEE, NEET, CUET coaching centres: Assam, Rajasthan have framed laws, but will they work?

anam-khan

JEE Main 2025 withheld results declared; NTA issues show cause notices ahead of action

Latest Question