Question

Two wires of different material and radius have their length in ratio of $1:2.$ if these were stretched by the same force$,$ the strain produced will be in the ratio$.$

• A. $4:1$
• B. $1:1$
• C. $2:1$
• D. $1:2$

Answer 1

The correct option is B $1:1$

We know that the young's modulus is given by$,$

$Y=stress/strain=\left(F/A\right)/strain$

$=>strain=F/AY$

where$,$

F $=$ force applied

A $=$ area of cross section

since the wires are made of same material so there young's modulus will be same$.$

Also the force applied and the area of cross section is same $($because radius is same$)$

Hence$,$

$strai{n}_1/strai{n}_2=F₁A₂Y₂/F₂A₁Y₁=1$

So$,$ the ratio of strain will be 1:1 despite of the ratio of length$.$

Hence,

option $\left(B\right)$ is correct answer.