Question

Mass M is distributed over a rod of length L. If the linear mass (lambda) linearly increases with length as lambda= kx. The moment of inertia of the rod about one end perpendicular to rod is
Kindly answer

Answer 1

linear mass density of the rod is given by

now we have

integrate both sides

so above is the total mass of rod

now by the formula of center of mass

now plug in value of mass of rod

so above is the position of center of mass of rod