A uniform sphere of radius R has a spherical cavity of radius `(R)/(2)` (see figure). Mass of the sphere with cavity is M. The sphere is rolling without sliding on a rough horizontal floor [the line joining the centre of sphere to the centre of the cavity remains in vertical plane]. When the centre of the cavity is at lowest position, the centre of the sphere has horizontal velocity V. Find: (a) The kinetic energy of the sphere at this moment. (b) The velocity of the centre of mass at this moment. (c) The maximum permissible value of V ( in the position shown ) which allows the sphere to roll without bouncing

A uniform sphere of radius R has a spherical cavity of radius `(R)/(2)

1.	A uniform sphere of radius R has a spherical cavity of radius `(R)/(2)` (see figure). Mass of the sphere with cavity is M. The sphere is rolling without sliding on a rough horizontal floor [the line joining the centre of sphere to the centre of the cavity remains in vertical plane]. When the centre of the cavity is at lowest position, the centre of the sphere has horizontal velocity V. Find: (a) The kinetic energy of the sphere at this moment. (b) The velocity of the centre of mass at this moment. (c) The maximum permissible value of V ( in the position shown ) which allows the sphere to roll without bouncing
Answer» Correct Answer - (a) `(31)/(40) MV^(2)` (b) `(15V)/(14)` (c) `V le sqrt(14 gR)`

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