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A thin rod, length L(0) at 0^(@)C and co...

A thin rod, length `L_(0)` at `0^(@)C` and coefficient of linear expansion `alpha` has its two ends mintained at temperatures `theta_(1)` and `theta_(2)` respectively Find its new length .

A

`L_(0)[1+alpha(theta_(1)+theta_(2))]`

B

`L_(0)(1 +alpha((theta_(1)+theta_(2))/(2)))`

C

`L_(0)(1+alpha theta_(1))`

D

`L_(0)(1 +alpha((theta_(1)+theta_(2))/(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
When temperature of a rod varies linearly then can be taken as mean of temperatures at the two ends According to the diagram
`theta = (theta_(1)+theta_(2))/(2)` Let temperature varies linearly in the rod from its one end to other end from `theta_(1) to theta_(2)` Let `theta` be the temperature of the mid-point of the rod Therefore, average temperature of the mod-point of the rod is
`rArr theta = (theta_(1)+theta_(2))/(2)`
Using relation `L =L_(0) (1 + alpha theta)`
or `L =L_(0)[1+alpha((theta_(1)+theta_(2))/(2))]`
.
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