Question

Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls smoothly from rest down a ramp and onto a horizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.504 m from the end of the ramp. The initial height of the object is H = 0.88 m; the end of the ramp is at height h = 0.13 m. The object consists of an outer cylindrical shell of a certain uniform density) that is glued to a central cylinder (of a different uniform density). The rotational inertia of the object can be expressed in the general form I = BMR2, but B is not 0.5 as it is for a cylinder of uniform density. Determine B. H T Number Units

Answer 1

=) Givenir d=0.504 m, H = 0.00m h = 0.13m Non Uniform Cylinder : I = $MR; B = ? I MR2 2 g 1] 1 1 29 (H - h) BMR² = MR² [29 (4- h) 1 B = 29 (4- n. use projectile motion equations, Time of flight, t > v² = q d² So purting this into eq" ß Now; we t = 2h ༥ g sh (H-h) x2h. = 1 29 (Han). gd² 4 h (H-h) d² al = 1

given values, - 1. 2 » Substituting the b = 4x0.13 few DRB-013) (0.504) After solving get; ТЕ we = 0.5 3.5 Ans.