Question

The resistance of a metallic wire is doubled by stretching it along its length.the ratio of initial to final length will be

Answer 1

Let the Original length, Resistance and area of the croos-section of the wire be l, R, and a respectively. 

∴ Resistivity(ρ₁) = Ra/l

Now,
New length = l'
New Resistance(R') = 2R
New area of the croos-section of the wire = a
[Since, it is not effected as per as the question].

∴ Resistivity(ρ₂) = 2R a/l'


We know, whether the area, length or the Resistance of the wire is increased or decreased, the Resistivity of the Wire will never changes. 

  ∴ ρ₁ = ρ₂
 Ra/l = 2Ra/l'
 1/l = 2/l'
 l/l' = 1/2
∴ l :l' = 1 : 2

Hence, the Ratio of the Initial to the Final length of the wire is 1 : 2.


Hope it helps.