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A non-uniform rod of length 0.5m is placed along the x-axis at a distance.2m from the origin. The mass per unit length 2 varies according to the expression λ = 5 + 2x2, measured in units of kg/m, where x is measured in meters from the origin. Set up but do not solve an integral that will allow you to find the gravitational force exerted by the rod on a 0.1 kg mass placed at the origin (Hint: An element of the rod has a mass dM - ldx). Be sure to include bounds on your integral. a. Find the value of the gravitational force on the mass using your integral above. b.
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