A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7 x , where x is _

Question

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7 x , where x is ______.

TestHub · Accepted Answer

In pure rolling work done by friction is zero. Hence, potential energy is converted into kinetic energy. Since initially the ring and the sphere have same potential energy, finally they will have same kinetic energy too.
$∴$ Ratio of kinetic energies $= 1$
$\Rightarrow \frac{7}{x} = 1 \Rightarrow x = 7$

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