Two wires of different materials each 2m long and of diameter 2mm are joined in series to
form a composite wire. If their young's moduli are 2 x 1011 N/m2 and 7 x 1011 N/m2 the
force required to produce a total elongation 0.9mm is
Answers
Explanation:
ANSWER
Given.
Length of both wires, L=2m
Radius of both wires, d=2mm=2×10
−3
m
Total extension of joined wire, ΔL
net
=0.9mm=9×10
−4
m
Both wires join in series, so tension in both is equal
T=
L
Y
1
AΔL
1
=
L
Y
2
AΔL
2
Net extension in joined wire.
⇒ΔL
net
=ΔL
1
+ΔL
2
=
Y
1
A
TL
+
Y
2
A
TL
=
A
TL
(
Y
1
1
+
Y
2
1
)
⇒ΔL
net
=
A
TL
(
Y
1
1
+
Y
2
1
)
⇒T=
L(
Y
1
1
+
Y
2
1
)
AΔL
net
=
2(
2×10
11
1
+
6×10
11
1
)
4
π
(2×10
−3
)
2
×9×10
−4
=212.05 N
Total force produced in joined wire is 212 N
Answer:
What force will produce a total extension of 0.9 mm. (Y1 = 2 × 1011 Pa & Y2 = 6 × 1011 Pa) . ... materials, each 2m long and of diameter 2mm, are joined in series to form a composite wire.
Explanation:
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Mechanical Properties of Solids
Elastic Potential Energy
Two wires of different mate...
PHYSICS
Two wires of different materials, each 2m long and of diameter 2mm, are joined in series to form a composite wire. What force will produce a total extension of 0.9mm. (Y
1
=2×10
11
Pa & Y
2
=6×10
11
Pa).
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ANSWER
Given.
Length of both wires, L=2m
Radius of both wires, d=2mm=2×10
−3
m
Total extension of joined wire, ΔL
net
=0.9mm=9×10
−4
m
Both wires join in series, so tension in both is equal
T=
L
Y
1
AΔL
1
=
L
Y
2
AΔL
2
Net extension in joined wire.
⇒ΔL
net
=ΔL
1
+ΔL
2
=
Y
1
A
TL
+
Y
2
A
TL
=
A
TL
(
Y
1
1
+
Y
2
1
)
⇒ΔL
net
=
A
TL
(
Y
1
1
+
Y
2
1
)
⇒T=
L(
Y
1
1
+
Y
2
1
)
AΔL
net
=
2(
2×10
11
1
+
6×10
11
1
)
4
π
(2×10
−3
)
2
×9×10
−4
=212.05 N
Total force produced in joined wire is 212 N