A particle of mass m is placed on the smooth face of an inclined plane of mas s M and slope $\theta$ which is free to slide on a smooth horizontal plane in a direction perpendicular to the edge. If the particle slides with an acceleration a, the acceleration of the inclined plane towards right A will be

detailed solution

Correct option is A

As the particle moves down the inclined plane, let a be its acceleration. Now the inclined plane moves horizontally towards right with acceleration A.Considering the vertical component of forces acting on the particle.mg−Rcos⁡θ=masin⁡θ    .......(i)For horizontal components the motion of the particle is considered at the accelerated frame. So a horizontal fictious force acts opposite to A. This pseudo force mA acts towards the left.Rsin⁡θ+mA=macos⁡θRsin⁡θ=m(acos⁡θ−A)     ......(ii)Now consider the force on inclined plane. The forces are shown in figure.Rsin⁡θ=MA          .....(iii)Rcos⁡θ+Mg=S  .........(iv) From equations (ii) and (iii), we get A=macos⁡θ(M+m)