Simple extension to problem by Nishant Rai

A uniform disc of mass \(m\) and radius \(R\) starts with a velocity \(v_{o}\) on a rough horizontal floor with a purely sliding motion at time \(t=0\). At time \(t=t_{o}\) disc starts rolling without sliding. Which of the following is/are true?

(A) Work done by frictional force up to time \( t \le t_0 \) is given by \( \frac{m \mu gt}{2} \left( 3 \mu gt - 2 v_0 \right) \).

(B) Work done by frictional force up to time \( t \le t_0 \) is given by \( \frac{m \mu gt}{2} \left( 2 \mu gt - 3 v_0 \right) \).

(C) Work done by frictional force up to time \( t =2t_0 \) is given by \({m \mu gt}\left( 3 \mu gt - 2 v_0 \right) \).

(D) Work done by frictional force up to time \( t =2 t_0 \) is given by \( \frac{m \mu gt}{2} \left( 3 \mu gt - 2 v_0 \right) \).

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