The figure above shows a solid sphere, cylinder, and hoop, all of the same mass and radius. If they are released from the top of the incline from rest, which object will reach the bottom first? All three objects will reach the bottom at the same time. The hoop. The sphere. The cylinder.
Question
The figure above shows a solid sphere, cylinder, and hoop, all of the same mass and radius. If they are released from the top of the incline from rest, which object will reach the bottom first? All three objects will reach the bottom at the same time. The hoop. The sphere. The cylinder.
Solution
The sphere will reach the bottom first. This is because of the distribution of mass in the different shapes. The sphere has its mass more evenly distributed, which allows it to roll down the incline faster. The cylinder, with its mass concentrated more towards the center, will roll down slower than the sphere. The hoop, with its mass concentrated furthest from the center, will roll down the slowest. This is due to the concept of rotational inertia, which states that an object with its mass distributed further from its axis of rotation will rotate slower than an object with its mass distributed closer to its axis of rotation.
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