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31 October, 07:41

Consider a small frictionless puck perched at the top of a xed sphere of radius R. If the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere?

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  1. 31 October, 07:54
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    Let the vertical height by which it descends be h. Let it acquire velocity of v.

    1/2 mv² = mgh

    v² = 2gh

    As it leaves the surface of sphere, reaction force of surface R = 0, so

    centripetal force = mg cosθ where θ is the angular displacement from the vertex.

    mv² / r = mg cosθ

    (m/r) x 2gh = mg cosθ

    2h / r = cosθ

    cosθ = (r-h) / r

    2h / r = r-h / r

    2h = r-h

    3h = r

    h = r / 3
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