A slender rod with length L has a mass per unit length that varies with distance from the left-hand end, where x=0 , according to dm/dx=γx , where γ has units of kg/m2 .
1.Calculate the total mass of the rod in terms of γ and L.
2.Use I=∫r2dm to calculate the moment of inertia of the rod for an axis at the left-hand end, perpendicular to the rod. Use the expression you derived in part A to express I in terms of M and L .
3.Repeat part B for an axis at the right-hand end of the rod.