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Linear mass density of a rod PQ of lengt...

Linear mass density of a rod PQ of length l and mass m is varying with the distance x (from P), as `lambda = (m)/(2l)(1+ax)`

(i) Determine the value of a
(ii) Also determine the distance of c.m. from the end P.

Text Solution

Verified by Experts

`dm = lambda dx`
`m = int_(0)^(l)(m)/(2l)(1+ax)dx " " rArr a = 2//l`
From P
`x_(cm)=(int xdm)/(m)=(int_(0)^(1)xx(m)/(2l)(1+(2x)/(l))dx)/(m)=(7)/(12)l`
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