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Three bodies a disc, a ring, a solid sphere of same radius, same mass are rolling down the same inclined plane without slipping. Which of three will reach the ground with minimum velocity ?

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To determine which of the three bodies (a disc, a ring, and a solid sphere) will reach the ground with the minimum velocity when rolling down an inclined plane without slipping, we can use the principle of conservation of energy. ### Step-by-Step Solution: 1. **Understanding the Problem**: We have three objects (a disc, a ring, and a solid sphere) of the same mass and radius rolling down an inclined plane. We need to find out which one reaches the bottom first in terms of velocity. 2. **Conservation of Energy**: The total mechanical energy at the top of the incline (potential energy) will be converted into kinetic energy at the bottom. The potential energy (PE) at height \( h \) is given by: \[ ...
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