A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be

Question

A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be (A) Proportional to l (B) inversely proportional to l (C) independent of l (D) independent of A

Tardigrade Admin · Accepted Answer

Let α= coefficient of thermal expansion, Y= Young modulus of the wire. If the wire is free to contract, its decrease in length would be l α t, where t= decrease in temperature. To maintain constant length, l α t becomes the effective elongation

Q. A metal wire of length $l$ and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be

Proportional to l

inversely proportional to l

independent of l

independent of A

Let $α =$ coefficient of thermal expansion,
$Y =$ Young modulus of the wire.
If the wire is free to contract,
its decrease in length would be $l α t,$
where $t =$ decrease in temperature.
To maintain constant length,
$l α t$ becomes the effective elongation

Q. A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be