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Two metal rods are fixed end to end betw...

Two metal rods are fixed end to end between two rigid supports, as shown in figure. Each rod is of length 'l' and area of cross-section is A. When the system is heated up, determine the conditioin whenthe juction between rods does not shift.
[Given, `Y_(1)` and `Y_(2)` are Young's modulus of materials of the rods, `alpha_(1)` and `alpha_(2)` are coefficient at linear expansion.

A

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

B

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

C

`alpha_(1) = alpha_(2)`

D

`Y_(1) = Y_(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Since each rod is prevented from expansion, so they are under compression and mechanical strain. The net strain in each rod.
`epsi_(1) = alpha_(1)//Delta T- (Fl)/(AY_(1))`
and `epsi_(2)= alpha_(2)//Delta T- (Fl)/(AY_(2))`
When `epsi_(1)= epsi_(2)= 0`
`rArr alpha_(1)//Delta T- (Fl)/(A Y_(1))= 0 and alpha_(2)//Delta T- (Fl)/(AY_(2))`
Solving we get
`alpha_(1) Y_(1)= alpha_(2) Y_(2)`
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