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A thin spherical shell of radius R lying...

A thin spherical shell of radius `R` lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?

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To solve the problem of where to hit a thin spherical shell so that it does not slip on a rough horizontal surface, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Problem**: We have a thin spherical shell of radius \( R \) resting on a rough horizontal surface. When it is struck by a cue, we need to determine the height \( H \) at which it should be hit to ensure that it rolls without slipping. 2. **Identify the Forces**: When the shell is hit, it experiences a force due to the cue and a frictional force from the surface. The frictional force will help in rolling the shell without slipping. ...
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