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Aplank of mass m1 with a uniform sphere of mass m2 placed on its rest on a smooth horizontal plane. A constant horizontal force F is applied to the plank . With that accelarations will the plank and the centre of the sphere move provided there is no sliding between the plank and sphere?

MIT 8.01 Physics I Classical Mechanics, Fall 1999
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Consider the plank and sphere as a system. total no: of forces acting on it : weight,mg, normal rctn, N and the afflied force F. as it is in vertical eqlbm., N=mg (newton's first law) theres is an acc. a in horizontal direction due to F. now consider sphere as a system. Here there are 3 forces- m2g, N2 and frictional force,f(its given that there is no slidng) . m2g=N f=m2a(sinc there is no relative motion b/w sphere and plank-no sliding-there acc are same) so net force = m2a and both wud move wid same acc.

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