A solid sphere and a hollow sphere of the same mass and of the same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be \( t_1 \) and \( t_2 \), respectively, then:
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When comparing rolling objects, recall that objects with less moment of inertia relative to their mass and radius will accelerate faster and reach the bottom of the incline in less time.
An object's time to roll down an incline is influenced by its moment of inertia. A solid sphere, possessing a lower moment of inertia than a hollow sphere, accelerates faster and consequently reaches the incline's base sooner. Based on rolling motion equations, the solid sphere's descent time will be shorter than the hollow sphere's due to its greater rotational inertia. Final Answer: \( t_1<t_2 \).
