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Two elastic rods are joined between fixe...

Two elastic rods are joined between fixed supports as shown in figure. Condition for no change in the lengths of individual rods with the increase of temperature `(alpha_(1),alpha_(2)`linear expansion coefficient, `A_(1),A_(2)` =area of rods, `Y_(1),Y_(2)` =Young’s modulus) is:

A

`(A_(1))/(A_(2)) =(alpha_(1)Y_(1))/(alpha_(2)Y_(2))`

B

`(A_(1))/(A_(2))=(L_(1)alpha_(1)Y_(1))/(L_(2)alpha_(2)Y_(2))`

C

`(A_(1))/(A_(2)) =(L_(2)alpha_(2)Y_(2))/(L_(1)alpha_(1)Y_(1))`

D

`(A_(1))/(A_(2))=(alpha_(2)Y_(2))/(alpha_(1)Y_(1))`

Text Solution

Verified by Experts

The correct Answer is:
D
`Y=("Stress")/("Strain")=(T//A)/(Deltal//l), T=(Y.Deltal)/(l)A=Y.A alphaDeltaT`
In both the rods tension will be same so
`T_(1)=T_(2)`
Hence, `Y_(1)A_(1)alpha_(1)DeltaT=Y_(2)A_(2)alpha_(2)DeltaT, (A_(1))/(A_(2))=(Y_(2)alpha_(2))/(Y_(1)alpha_(1))`
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