Question

The Young's modulus of a wire of length L and radius r is Y. If the length is reduced to half, what will be its Young's modulus?

Answer 1

Answer:

original young's modulus Y=f/a×l/∆l

This can be written as Y=f/πr^2×l/∆l-(1)

New young's modulus Y'=f/π(r/4)^2×l/2/∆l

That is Y'=16f/πr^2×l/∆l×1/2

That is Y'=16×1/2×f/πr^2×l/∆l-(2)

Substituting (1) in (2) we get

Y'=8Y