Let it roll

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


M=4 kgM=4~kg, m=2 kgm=2~kg, μ=0.6\mu=0.6, g=10 m/s2g=10~m/s^2,v=5 m/sv_{\circ}=5~ m/s, F=40 NF=40~N.

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