The block of mass m is in equilibrium relative to the smooth wedge of mass M which is pushed by a horizontal force F. Find pseudo force acting on (a) m, (b)M as viewed by the observer sitting on the wedge. Will these pseudo forces (c ) equal and opposite, action reaction pairs? Explain.

Explanation

Taking block and wedge as system.
Net force on the system horizontally =F
Total mass `=M+m`
Therefore, acceleration of the system in +ve x-direction.
`a=(F)/(M+m) implies vec(a)=(f)/(M+m) hat(i)`
(a) Pseudo force acting on block m is in opposite direction of observer acceleration and magnitude equal to multiplication of mass of the object and the acceleration of the observer
`vec(F)_(PS)=-ma hat(i) = -(mF)/(M+m)hat(i)`
(b) Pseudo force acting on block `M vec(F')_(PS)=-Ma hat(i)`
(c ) Pseudo force is not a real force. It is applied to solve the problem of non-inertial frame. It does not have action-reaction pairs.