Question

Two wires `A` and `B` have equal lengths and aremade of the same material , but diameter of wire `A` is twice that of wire `B`. Then, for a given load,
A. (A) the extension of `B` will be four times that of `A`
B. (B) the extensions of `A` and will be equal
C. (C) the strain in `B` is four times that in `A`
D. (D) the strains in `A` and `B` will be equal

Answer 1

Correct Answer - A::C
Area of cross- section is `A = (pid)^(2)/4 DeltaL = (F)/(pid^(2) //4).L/Y`
`rArr DeltaL prop 1/d^(2)`
`:.(DeltaL_(B))/(DeltaL_(A)) = ((2d)^(2) )/(d)^(2) `
`rArr DeltaL_(B) = 4 Delta L_(A) `
Strain `= DeltaL/L = (4F)/(pid^(2)Y`
` rArr` Strain `prop 1/d^(2)`
`:. ("strain")_(B) =4 ("strain" )_(A)`