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SOLVED:The sphere has two types of motion, one is the rotation about its own axis and the other is motion in a circle of radius R. Hence the sought kinetic energy T=(1)/(2) I1 ω1^2 (1)/(2) I2 ω2^2 where I1 is the moment of inertia about its own axis, and I2 is the moment of inertia about the vertical axis, passing through O, But, I1=(2)/(5) m r^2 and I2=(2)/(5) m r^2 m R^2 (using parallel axis theorem,) In addition to ω1=(v)/(r) and ω2=(v)/(R) Using (2) and (3) in (1), we get T^'=(7)/(10) m v^

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