Three bodies, a thin ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are same. Which of the bodies reaches the ground with maximum velocity?

Question

Three bodies, a  thin ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are same. Which of the bodies reaches the ground with maximum velocity?

Infinity Learn · Accepted Answer

According to conservation of mechanical energy or        $$mgh$$ $$=$$ $$12mv2(1+k2R2)$$           $$v2$$ $$=$$ $$(2gh1+k2R2)It$$ is independent of the mass of the rolling body.For a ring, $$k2$$ $$=$$ $$R2$$     vring $$=$$ $$2gh1+1$$ $$=$$ ghFor a solid cylinder, $$k2$$ $$=$$ $$R22vcylinder=$$ $$2gh1+12$$ $$=$$ $$4gh3For$$ a solid sphere, $$k2$$ $$=$$ $$25R2vsphere$$ $$=$$ $$2gh1+25$$ $$=$$ $$10$$ $$gh7Among$$ the given three bodies the solid sphere has the greatest and the ring has the least velocity at the bottom of the inclined plane.

Three bodies, a thin ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are same. Which of the bodies reaches the ground with maximum velocity?

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