Question

the ratio of radius of two wires of same material is 2:1 . if they are stretched by applying similar force then what would be ratio of the stress generated ?

Answer 1

Answer:

As we know,

Stress = \frac{Force}{Area}

Area = π r ²,

where r is the radius

A ∝ r²

\frac{A_{1} }{A_{2}}  = \frac{r_{1} }{r_{2}} ^{2}

Given,

r1 : r2 = 2 : 1

\frac{A_{1} }{A_{2}}  = \frac{2 }1} ^{2}

\frac{A_{1} }{A_{2}}  =\frac{4}{1}

Now,

\frac{S_{1} }{S_{2}}= \frac{F_{1} /A_{1} }{F_{2} /A_2} }

Since F₁ = F₂ = F

So,

\frac{S_{1} }{S_{2}} = \frac{F /A_{1} }{F /A_2} }

\frac{S_{1} }{S_{2}} = \frac{A_{2} }{A_{1}}

\frac{S_{1} }{S_{2}} = \frac{1}{4}

Therefore, ratio S₁ : S₂ = 1 : 4