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(B) The velocity of a body rolling down an inclined plane is given by $v = \sqrt{\frac{2gh}{1 + \frac{k^2}{R^2}}}$,where $k$ is the radius of gyration

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The solid sphere reaches the bottom with greater speed.

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(B) The velocity of a body rolling down an inclined plane is given by $v = \sqrt{\frac{2gh}{1 + \frac{k^2}{R^2}}}$,where $k$ is the radius of gyration.For a solid sphere,$k^2 = \frac{2}{5}R^2$,so $v_{solid} = \sqrt{\frac{2gh}{1 + 0.4}} = \sqrt{\frac{2gh}{1.4}}$.For a hollow sphere,$k^2 = \frac{2}{3}R^2$,so $v_{hollow} = \sqrt{\frac{2gh}{1 + 0.67}} = \sqrt{\frac{2gh}{1.67}}$.Since the denominator for the solid sphere is smaller,the solid sphere reaches the bottom with a greater speed.Both spheres start from the same height,so their potential energy $mgh$ is the same. Since the total energy is conserved,the total kinetic energy (translational + rotational) at the bottom is the same for both.

$A$ hollow sphere and a solid sphere having the same mass and same radius are rolled down a rough inclined plane. Which of the following statements is correct?

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