Question

7. Answer the following questions. [10 pt] а. A solid sphere of mass 2 kg and radius 30 cm rolls down an incline without slipping. If the incline is 5 m high, how fast is the ball going at the bottom? b. A 500 g hoop with diameter 1.2 m is rolled down the same hill. If it too rolls without slipping, how fast is the hoop going at the bottom of the hill? c.Show that if the moment of inertia is given by I = CMR² , where c is a factor dependent on the shape of the object, that the acceleration down the incline is given by a=\left(\frac{1}{1+c}\right) g \sin \theta d. List two additional shapes with similarly formatted moments of inertia that could be rolled down the same hill. Rank all four (your two shapes, the sphere, and the hoop) in order of smallest to largest acceleration.

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