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1. A thin rod of length L and total mass M has a linear mass density that varies with position as λ(x)-γ?, where x = 0 is located at the left end of the rod and γ has dimensions M/L3. ĮNote: requires calculus] (a) Find γ in terms of the total mass M and the length L. (b) Calculate the moment of inertia of this rod about an axis through its left end, oriented perpen dicular to the rod; expressed in terms of M and L (c) Determine the moment of inertia of this rod about an axis through its right end, oriented per- pendicular to the rod; expressed in terms of M and L

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(a) lonsideu an element dx 2 3ML take uigut end a oaigiu as axis shifts thee 3 5 2 30 L3 52 30o X-レ ML 10

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