A uniform solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is struck by a horizontal cue at a height h above the center. For the sphere to roll without slipping immediately after the impact, the value of h must be:
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Key Exam Tip:
The condition for rolling without slipping is $v = \omega R$. Use impulse-momentum theorems for both linear ($J=Mv$) and angular ($Jh=I\omega$) motion to relate the impact height to the sphere's properties.