Q.
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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a
(M+m)gtanθ
b
(M+m)gcotθ
c
mM(M+m)gtanθ
d
mM(M+m)gcotθ
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; Ncosθ=mg ...(i)and F−Nsinθ=ma ...(ii)From FBD of wedge; Nsinθ=Ma...(iii)from equations (i), (ii) and (iii)solving we get F=mM(M+m)gtanθ
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