Question

The length of wire increases by 9 mm when weight of 2.5 kg is hung from the free end of wire. If all conditions are kept the same and the radius of wire is made thrice the original radius, find the increase in length. (Ans : 1 mm)

Answer 1

let the length of wire is L

change in length of wire after loading weight 2.5kgwt at one end , ∆L = 9mm

We know,
Young's modulus, Y = $\frac{FL}{A\Delta{L}}$
or, Y = FL/(πr²∆L)

if Y, F and L are constant terms.

then, ∆L is inversely proportional to r².

so, $\frac{\Delta{L}}{\Delta{L}'}=\frac{r'^2}{r^2}$

a/c to question,
the radius of wire is made thrice the original radius. e.g., r' = 3r

hence, ∆L/∆L' = (3r)²/r²

9mm/∆L' = 9r²/9 = 9

∆L' = 1mm

Answer 2

Answer:

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