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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,it reaches the bottom with a greater speed.Both spheres start from the same height,so their potential energy is the same. By the law of conservation of energy,the total kinetic energy at the bottom will be 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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