Question

If the radius of wire stretched by a load is doubled then its young's modulus will be

Answer 1

Since Y is inversely proportional to r².
So Y' is 4 times Y.
Hope this helps... :)

Answer 2

Answer:

The new young's modulus will be one fourth of original young's modulus.

Explanation:

Given that,

Radius r = 2 r

We know that,

The formula of young's modulus

$Y=\dfrac{FL}{A\Delta L}$

$Y = \dfrac{FL}{\pi\times r^2\times \Delta L}$......(I)

If the radius of wire stretched by a load is doubled

Then the young's modulus

$Y'= \dfrac{FL}{\pi\times (2r)^2\times\Delta L}$

$Y'=\dfrac{FL}{\pi\times4r^2\times\Delta L}$......(II)

From equation (I) and (II)

$\dfrac{Y}{Y'}=4$

$Y'=\dfrac{Y}{4}$

Hence, The new young's modulus will be one fourth of original young's modulus.