Question

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

(a) MgL
₁ /AL


(b) Mg(L₁ - L)
/AL



(c) MgL
/AL₁


(d) MgL
/A(L₁ - L)​

Answer 1

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

To Find:-

• Find the expression for Young' modulus.

Solution:-

As we know that:-

• $\sf \: Y = \dfrac { \: \: FL_o \: } { A∆l }$

Now ,

We have to Substitute the Values:-

$\sf\longrightarrow \: Y = \dfrac { mg \times L } { A( L_1 - L ) }$

$\sf\longrightarrow \: Y = \dfrac { mgL } { A( L_1 - L ) }$

Hence ,

• Option D is correct

Answer 2

Explanation:

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 L1

We know that the Young's modulus is given as:

Y=FL°/A delta l

Here , L° is the initial length of wire and delta l

is the chnage in length of wire.

Substitute the values:

Y=mg×L/A(L1-L)

so Y= mgl / A( L1-L)