# Let it roll

A plank of mass $$M$$ is moving on a smooth horizontal surface with speed $$v_{\circ}$$. At time $$t=0$$, a sphere of mass $$m$$ and radius $$r$$ is gently placed on it and simultaneously. A constant horizontal force $$F$$ is applied on the plank in the opposite direction of $$v_{\circ}$$. Find the time at which sphere starts pure rolling on the plank . The coefficient of friction between the plank and sphere is $$\mu$$.

$$M=4~kg$$, $$m=2~kg$$, $$\mu=0.6$$, $$g=10~m/s^2$$,$$v_{\circ}=5~ m/s$$, $$F=40~N$$.

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