A man of mass $60\ kg$ is standing on a platform of mass $40\ kg$ as shown in figure then what force man should apply on rope so that he accelerate up with the platform with acceleration of $2\ m/s^2$ ............ $N$

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction, as shown in figure. If the trolley is accelerated horizontally along the positive $x$ -axis with $a_0$, then If $a_{min}$ and $a_{max}$ are the minimum and maximum values of $a_0$ for which the blocks remain stationary with respect to the surface, then identify the correct statements

In the arrangement shown in figure $a _{1}, a _{2}, a _{3}$ and $a _{4}$ are the accelerations of masses $m _{1}, m _{2}, m _{3}$ and $m _{4}$ respectively. Which of the following relation is true for this arrangement?

Two equal masses $A$ and $B$ are arranged as shown in the figure. Pulley and string are ideal and there is no friction. Block $A$ has a speed $u$ in the downward direction. The speed of the block $B$ is :-

A balloon of mass $m$ is descending down with an acceleration $\frac{g}{2}$.  How much mass should be removed from it so that it starts moving up with same acceleration?

In the figure shown the block $B$ moves down with a velocity $10 m/s$. The velocity of $A$ in the position shown is ......... $m/s$