A heavy ball is thrown on a rough horizontal surface in such a way that it slides with a speed $V_{0}$ initially without rolling. It will roll without sliding when its speed fall to :

(2 / 7) V_{0}

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(3 / 7) V_{0}

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(5 / 7) V_{0}

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(7 / 5) V_{0}

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Solution

The correct option is C $(5 / 7) V_{0}$
Angular momentum conservation will apply here.
Initial angular momentum $= m V_{o} r$
Moment of inertia about centre $= (2 / 5) m r^{2}$
Let final velocity be V.
There final momentum $= I (V / r) + m V r$
Therefore, $m V_{o} r = (2 / 5) m V r + m V r$
$V = 5 / 7 V_{o}$

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A heavy ball is thrown on a rough horizontal surface in such a way that it slides with a speed V0 initially without rolling. It will roll without sliding when its speed fall to :

The correct option is C (5/7)V0Angular momentum conservation will apply here.Initial angular momentum =mVorMoment of inertia about centre =(2/5)mr2Let final velocity be V.There final momentum =I(V/r)+mVrTherefore, mVor=(2/5)mVr+mVrV=5/7Vo

A heavy ball is thrown on a rough horizontal surface in such a way that it slides with a speed $V_{0}$ initially without rolling. It will roll without sliding when its speed fall to :