Question

A block of mass $m$ is kept on a wedge of mass $M$. Initially the system is held. At certain time the system is released and the wedge is observed to move with acceleration $A$ on inclined surface as shown. There is no friction anywhere. The acceleration of block $\left(m\right)$ with respect to wedge $\left(M\right)$ will be

• A. $A$ rightward
• B. $A\cos \theta$ rightward
• C. $A\cos \theta$ leftward
• D. none of these

Answer 1

The correct option is B $A\cos \theta$ rightward

Considering the small block with mass $\text{m}$. Its free body diagram can be given as

As we can see there is no horizontal force on mass $\text{m}$
So it has no horizontal motion as seen from the ground frame of reference.
Now if we change the frame of reference and take it as wedge, then the mass $\text{m}$ will appear as moving away from wedge. Now if we consider pseudo force in direction opposite to the motion of wedge of mass $\text{M}$, then its acceleration would be in Northeast direction as refer to the diagram. But as the vertical velocity of both the masses is same as they are connected to each other.
So horizontal component of the pseudo force will act and its acceleration would be $Acos\theta$ rightward