An iron rod is fitted along the diameter of a circular iron ring. Explain, whether the ring remains circular or not, when the system is heated.

Explanation

The ring will continue to be circular even when the system is heated.
Let the initial diameter of the ring be d and the coefficient of linear expansion be `alpha.`
`therefore` Circumference of the ring `=pid` and length of the rod = d.
`therefore" ""length of the circumference of the ring"/"length of the rod"=(pid)/d=pi`
When the system is heated to a temperature `theta`,
the new circumference `=pid(1+alphatheta)` and the new length `=d(1+alphatheta)`
`therefore` The new ratio `=(pid(1+alphatheta))/(d(1+alphatheta))=pi`
Hence, the ring continues to be circular.