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A solid sphere of mass M and radius R resting on a smooth horizontal surface is given a sharp horizontal impulse at a height h above the ground. The sphere immediately begins to roll without slipping on the surface. What is the value of h?
- (A) h = 7R/5
- (B) h = 2R/5
- (C) h = R
- (D) h = 5R/7
Correct answer: (A) h = 7R/5
Solution
A horizontal impulse J applied at height h produces linear momentum Mv = J and angular momentum change about the centre equal to J*(h - R). For pure rolling, v = omega*R, so omega = v/R. Setting the angular impulse equal to I*omega with I = (2/5)MR² gives h = 7R/5.
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