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A composite wire of a uniform cross-sect...

A composite wire of a uniform cross-section `5.5xx10^(-5)m^(2)` consists of a steel wire of length `1.5m` and a copper wire of length `2.0m`. The amount of stretch when it it loaded with a mass of `200kg` is [Young's modulus of steel is `2xx10^(11)Nm^(-2)` and that of copper is `1xx10^(11)Nm^(-2)` .
Take `g=10ms^(-2)`

A

`1mm`

B

`2mm`

C

`3mm`

D

`4mm`

Text Solution

Verified by Experts

The correct Answer is:
A
Since the steel and copper parts of the wire are of the same cross-sectional area (A) and are loaded with the same weight `F=Mg`, they are under the same stress `((F)/(A))`.
Therefore, `(Y_(s)l_(s))/(L_(s))=(Y_(c )l_(c ))/(L_(c ))=(F)/(A)=(Mg)/(A)` or `l_(s)=(Mg)/(A).(L_(s))/(Y_(s))` and `l_(c )=(Mg)/(A)(L_(c ))/(Y_(c ))`
`:.` extension of the composite wire is
`l=l_(s)+l_(c )=(Mg)/(A)((L_(s))/(Y_(s))+(L_(c ))/(Y_(c )))`
substituting the given values we find `l=10^(-3)m=1mm`
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