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A metal rod of Young's modulas Y and coe...

A metal rod of Young's modulas `Y` and coefficient of thermal expansion `alpha` is held at its two ends such that its length remains invariant. If its temperature is raised by `t^(@)c`, then the linear stress developed in it is

A

`(Y)/(alphat)`

B

`Y alpha t`

C

`(1)/((Y alpha t))`

D

`(alpha t)/(Y)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(Deltal)/(l) = alpha. Delta T`
and `Y = (F//A)/(Deltal//l)`

So, `F = A Y alphat`
Thermal stress `((F)/(A)) = Y alphat`.
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