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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(M+m)gtan⁡θ

(M+m)gcot⁡θ

mM(M+m)gtan⁡θ

mM(M+m)gcot⁡θ

answer is C.

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Detailed Solution

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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