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

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

A

1 mm

B

2mm

C

3 mm

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 wrie 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 =1 `mm
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