. A slender rod with length Lhas a mass per unit length that varies with distance from the left end, where 푥=0, according to 푑푚/푑푥=훾푥, where 훾has units of kg/m2.a) Calculate the total massMof the rod in terms of 훾and L. b) Use the equation 퐼=∫푟=푑푚to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Express your resultinterms of Mand L.(Hint: Revise the problem-solving section 9)c) Assume that the rodwithlength퐿=0.4푚andmass푀=3.0푘푔is rotating about theaxis as in part b. The angle through which the rod has turned varies with time according to휃(푡)=(1.1푟푎푑푠⁄)푡+(6.3푟푎푑푠=⁄)푡=.Wh at is the kinetic energy of the rod when it hasrotated0.1 rev? (Note: 1푟푒푣=2휋푟푎푑)