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A rod, of length L at room tempera ture ...

A rod, of length L at room tempera ture and uniform area of cross section A, is made of a metal having coefficient of linear expansion `alpha//""^(@)C`. It is observed that an external compressive force F, is applied on each its ends, prevents any change in the length of the rod, when its temperature rises by `DeltaTK.` Young's modulus, Y, for this metal is :

A

`(2F)/(A alpha Delta T)`

B

`(F)/(A alpha (Delta T- 273))`

C

`(F)/(A alpha Delta T)`

D

`(F)/(2A alpha Delta T)`

Text Solution

Verified by Experts

The correct Answer is:
C
`Delta L= L alpha Delta T`
Strain `= (Delta L)/(L)= alpha Delta T`
`Y= ("Stress")/("Strain")= (F)/(A alpha Delta T)`
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