A rod of length L has non-uniform linear mass density given by where a and b are constants and The value of x for the centre of mass of the rod is at
Question
A rod of length L has non-uniform linear mass density given by
where a and b are constants and
The value of x for the centre of mass of the rod is at
Solution
The question seems to be incomplete. However, I can guide you on how to find the center of mass for a rod with non-uniform linear mass density.
The center of mass (x_cm) for a one-dimensional object like a rod is given by the integral of xdm over the total mass of the object.
If the linear mass density of the rod is given by λ(x) = ax + b, then the differential mass element dm at position x along the rod is given by dm = λ(x)dx = (ax + b)dx.
The total mass of the rod M is given by the integral of dm from 0 to L, which is ∫(from 0 to L) (ax + b) dx.
The x-coordinate of the center of mass x_cm is given by (1/M) ∫(from
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