Question 14: Properties of Matter

Question

The Young's modulus of steel wire of radius $r$ and length $L$ is $Y$.
If the radius $r$ and length $L$ of the wire are doubled then the value of $Y$

Accepted Answer

YoungÃ¢ÂÂs modulus is a property of the material itself. It does not depend on the length or radius of the wire.
We know,
$$ Y = \frac{	ext{longitudinal stress}}{	ext{longitudinal strain}} $$
or,
$$ Y = \frac{F/A}{\Delta L/L} = \frac{FL}{A \Delta L} $$
Here, $A = \pi r^2$ is the area of cross-section.
Even if the radius $r$ and length $L$ are doubled, YoungÃ¢ÂÂs modulus $Y$ of the steel wire does not change, because it depends only on the material, that is, steel.
So, the correct answer is:
$$ \boxed{	ext{Option C: remains unchanged}} $$

Answer

increases by two times

Answer

reduces by half

Answer

remains unchanged

Answer

becomes one fourth

Properties of Matter

The Young's modulus of steel wire of radius r and length L is Y. If the radius r and length L of the wire are doubled then the value of Y

Choose the correct answer: