Question

a steel wire of length L area of cross section A has a young's modulus Y at a given Temperature. Then the young's modulus of another steel wire of length 2L and area of cross - section A/2 at the same temperature is,​

Answer 1

Answer:

Explanation:

Correct option is

A

The work done by F is

2L

YAl

2

C

The elastic potential energy stored in the wire is

2L

YAl

2

D

No heat is produced during the elongation

We have

l=

AY

FL

or

F=

L

AY

l

Work done is given using the relation

dW=Fdx

or

dW=

L

AY

xdx

or

W=

L

AY

∫

0

l

xdx

or

W=

2L

AYl

2

The elastic potential energy is given as ΔU=W

or

ΔU=

2L

AYl

2

(This is the energy stored in the wire).

All the work done on the wire is stored as its potential energy, thus there is no heat produced during elongation