A block of mass m lies on wedge of mass M, which lies on fixed horizontal surface. The wedge is free to move on the horizontal surface. A horizontal force of magnitude F is applied on block as shown, neglecting friction at all surfaces, the value of force F such that block has no relative motion w.r.t. wedge will be: (where$$ g is acceleration due to $$gravity)

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Infinity Learn · Accepted Answer

For no relative motion between wedge and block, let the acceleration of both block and wedge be 'a' towards left.From FBD of block; Ncos⁡θ$$=mg$$ ...(i)and$$ F−Nsin⁡θ$$=ma$$ ...$$(ii)From$$ FBD of wedge; Nsin⁡θ$$=Ma$$...$$(iii)from$$ equations $$(i), (ii) and $$(iii)solving$$ we get $$F=mM(M+m)gtan$$⁡θ

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