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Two rods are joined between fixed suppor...

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the length of individual rods with the increase of temperature will be
`"(" alpha_(1), alpha_(2)=` linear expansion coefficient
`A_(1), A_(2)=` Area of rods
`Y_(1), Y_(2)=` Young modulus `")"`

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 alpha DeltaT`
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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