A uniform disc of mass \( m \) and radius \( R \) is projected horizontally with velocity \( v_{...

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A uniform disc of mass \( m \) and radius \( R \) is projected horizontally with velocity \( v_{0} \) on a rough horizontal floor so that it starts with a purely sliding motion at \( t=0 \). After \( t_{0} \) seconds it acquires a purely rolling motion.
(a) Calculate the velocity of the centre of mass of the disc at \( t_{0} \).
(b) Assuming the coefficient of friction to be \( \mu \), calculate to. Also calculate the work done by the frictional force as a function of time and the total work done by it over a time \( t \) much longer than \( t_{0} \).
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