# 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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