A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L1 when mass M is suspended from its free end. The expression for Young’s modulus is:

Question

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L1 when mass M is suspended from its free end. The expression for Young’s modulus is: (A)  (MgL1/AL) (B)  (Mg(L1-L)/AL) (C)  (MgL/AL1) (D)  (MgL/A(L1-L))

Tardigrade Admin · Accepted Answer

When the new mas 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 the Young's modulus is given as:
$Y =\frac{ FL _{ o }}{ A \Delta l }$
Here, $L_{o}$ is the initiallength of wire and $\Delta l$ is the chnage in length of wire.
Substitute the values:
$Y =\frac{ mg \times L }{ A \times\left( L _{1}- L \right)}$
So, $Y=\frac{m g L}{A\left(L_{1}-L\right)}$

Q. 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:

$\frac{M g L _{1}}{A L}$

$\frac{M g ( L _{1} - L )}{A L}$

$\frac{M gL}{A L _{1}}$

$\frac{M gL}{A ( L _{1} - L )}$

Q. A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L1​ when mass M is suspended from its free end. The expression for Young’s modulus is:

ALMgL1​​

ALMg(L1​−L)​

AL1​MgL​

A(L1​−L)MgL​

Q. 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:

$\frac{M g L _{1}}{A L}$

$\frac{M g ( L _{1} - L )}{A L}$

$\frac{M gL}{A L _{1}}$

$\frac{M gL}{A ( L _{1} - L )}$