A 1 m long wire is broken into two unequal parts X and Y The X part of the wire is streched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

Question

A 1 m long wire is broken into two unequal parts X and Y The X part of the wire is streched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y. (A) 1: 4 (B) 1: 2 (C) 4: 1 (D) 2: 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/15cb1a3b2c6e03a2dc47a1d974f35d5f-.png" /> ( R X / R Y )=(ℓ X /ℓ Y ) When wire is stretched to double of its length, then resistance becomes 4 times R W =4 R X =2 R Y ( R X / R Y )=(1/2) So. (ℓ X /ℓ y )=(1/2)

Q. A $1 m$ long wire is broken into two unequal parts $X$ and $Y$ The $X$ part of the wire is streched into another wire W. Length of $W$ is twice the length of $X$ and the resistance of $W$ is twice that of Y. Find the ratio of length of $X$ and $Y$ .

$1 : 4$

$1 : 2$

$4 : 1$

$2 : 1$

$\frac{R _{X}}{R _{Y}} = \frac{ℓ _{X}}{ℓ _{Y}}$
When wire is stretched to double of its length, then resistance becomes 4 times
$R_{W} = 4 R_{X} = 2 R_{Y}$
$\frac{R _{X}}{R _{Y}} = \frac{1}{2}$
So. $\frac{ℓ _{X}}{ℓ _{y}} = \frac{1}{2}$

Q. A 1m long wire is broken into two unequal parts X and Y The X part of the wire is streched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

1:4

1:2

4:1

2:1