Question

A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young's modulus is :

• A. $\frac{MgL}{A{L}_1}$
• B. $\frac{MgL}{A(L_1-L)}$
• C. $\frac{Mg{L}_1}{AL}$
• D. $\frac{Mg(L_1-L)}{AL}$

Answer 1

The correct option is B $\frac{MgL}{A(L_1-L)}$


When the new mass is hanged to the wire, the force exerted on the wire is :
$F=Mg$

The initial length of the wire is $L$ and the new length is $L_1$.

We know that Young's Modulus is given as :
$Y=\frac{FL}{A\Delta L}$

Where $L$ is the initial length of wire and $\Delta L$ is the change in length of the wire.

Now, put all the values in the above formula, we get,

$Y=\frac{MgL}{A(L_1-L)}$