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A solid sphere of mass M and radius r slips on a rough horizontal plane. At some instant it has translational velocity $v_{0}$ and rotational velocity about the centre $\frac{v_{0}}{2 r}$ . The translational velocity after the sphere starts pure rolling is

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6v07 in forward direction

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detailed solution

Correct option is A

Angular momentum can be conserved about lowest pointmv0r + 25mr2v02r = mv'r+25mr2v'r10mv0r+2mv0r10 = 7 mv'r5v' = 6v07

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A solid sphere of mass M and radius r slips on a rough horizontal plane. At some instant it has translational velocity v0 and rotational velocity about the centre v02r. The translational velocity after the sphere starts pure rolling is

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A solid sphere of mass M and radius r slips on a rough horizontal plane. At some instant it has translational velocity $v_{0}$ and rotational velocity about the centre $\frac{v_{0}}{2 r}$ . The translational velocity after the sphere starts pure rolling is