A rod has variable co-efficient of linear expansion `alpha = (x)/(5000)`. If length of the rod is `1` m . Determine increase in length of the rod in (cm) on increasing temperature of the rod by `100^(@)C`.

Answer

1

Explanation

Increase in length of dx = `alpha l_(0)DeltaT= ((x)/(5000))("dx")(100) = (x)/(50)dx`
`implies ` Total thermal expansion = `int_(0)^(1)(x)/(50)dx = ((x^(2))/(100))_(0)^(1) = (1)/(100)"m" = 1cm`