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A rod of length L is placed along the x-...

A rod of length L is placed along the x-axis between x=0 and x=L. The linear mass density is `lambda` such that `lambda=a+bx`. Find the mass of the rod.

Text Solution

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We take air element dx on the rod at distance x from origin.

Mass of element,
`dm=(a+bx)dx`
Total mass , `M= int dm= int _(0)^(L)(a+bx)dx`
`=a[x]_(0)^(L)+b[(x)^(2)/(2)]_(0)^(L)=aL+ (bL^(2))/(2)`
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