Solid sphere and hollow sphere rolled down an inclined plane

AI Thread Summary
A solid sphere and a hollow sphere of the same mass and radius were analyzed as they rolled down a rough inclined plane. The discussion confirms that the solid sphere reaches the bottom with a greater speed due to its lower moment of inertia, which allows it to convert more gravitational potential energy into translational kinetic energy. While the solid sphere has a higher velocity, it does not necessarily have greater kinetic energy than the hollow sphere when considering both translational and rotational components. The confusion arises from the interpretation of kinetic energy in relation to speed and the distribution of mass. Ultimately, the solid sphere's advantage lies in its speed, not in a higher total kinetic energy.
Yatin
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A solid sphere and a hollow one of same mass and radii are rolled down a rough inclined plane.
Which of the following is true?
(A) solid sphere reaches bottom with greater speed.
(B) solid sphere reaches the bottom with greater kinetic energy.

( I know that option A is correct.Thus I felt that B should also be correct.
However A is the only option given in the book as correct. Please help)
 
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Why do you think the kinetic energy of the solid sphere is greater? Because of its higher velocity? If this is the case, maybe another look at the statement helps: it says ' [...] are rolled down [...] '.
 
See the above but even in that case V at the end = V initial + the acceleration due to gravity that is experienced by both balls; or, is there something else I am also missing?
 
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