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,
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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
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