Pseudo Force

Assuming all the surfaces to be frictionless, calculate the horizontal force $F$ that must be applied to $m_3$, so that $m_1$ and $m_2$ do not move relative to $m_3$.

Find the mass $M$ of the hanging block shown in the figure, which will prevent the smaller block from slipping over the triangular block. (All the surfaces are frictionless and the strings and the pulleys are light.)

Body $A$ is placed on a frictionless wedge making an angle $\theta$ with the horizontal. The horizontal acceleration towards left to be imparted to the wedge for the body $A$ to freely fall vertically is

A triangular block of mass $M$ rests on a smooth surface as shown in the figure, a cubical block of mass $m$ rests on it. What horizontal force must be applied to $M$ so as to keep $m$ stationary relative to $M$?

An object kept on a smooth inclined plane of inclination $\theta$ with horizontal, can be kept stationary relative to the incline by giving a horizontal acceleration to the inclined plane equal to

A block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block has a magnitude