Question

The youngs modulus of a wire of lwngth l and radius r is y. If the length is redused by l/4 and radius r/2 what will be its youngs modulus?

Answer 1

It's Young's modulus increased by 4 times because Young's modulus is inversely proportional to the length

Answer 2

Young's modulus is constant for a given material.

Definition of Young's modulus is:

Y = stress / strain = (F / A) / (l / L)

where F = applied force, A = area, l = change in L, L = length

or Y = (F * L) / (A * l)

then (F * L1) / (A1 * l1) = (F * L2) / (A2 * l2)

for the same applied force    (L1 * A2 * l2) = (L2 * A1 * l1)

l2 / l1 = (L2 * A1) /  (L1 * A2) = (L2 / L1) * (A1 / A2)

If A2 = A1 / 4   and L2 = L1 / 4    

l2 / l1 = (1 / 4) * 4 = 1

so the wire would undergo the same elongation

if the length is 1/4 the original length and the area 1/4 the original area