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A copper rod and steel rod having length...

A copper rod and steel rod having length `L_(c)` and `L_(s)` respectively at certain temperature. It is observed that difference between their length remains constant at all temperature. If `alpha_(c)` and `alpha_(s)` ar their respective coefficient of linear expansions. Then, ratio of `L_(s)/L_(c)` is `

A

`alpha_(c)/alpha_(s)`

B

`alpha_(s)/alpha_(c)`

C

`(1+alpha_(s)/alpha_(c))`

D

`(1+alpha_(c)/alpha_(s))`

Text Solution

Verified by Experts

a) If rods are heated at `Deltat^(@)`C, the increase in length of steel and copper rods are
`DeltaL_(s) = L_(s)alpha_(s)Deltat`, and `DeltaL_(c) = L_(c)alpha_(c)DeltaT`
Difference between their lengths will remain constant.
`rArr DeltaL_(s) = DeltaL_(c)`
`rArr L_(s)alpha_(s)DeltaT=L_(c)alpha_(c)Deltat` or `L_(s)/L_(c)=(alpha_(c)/alpha_(s)`
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