A trolley of mass $8 \mathrm{kg}$ is standing on a frictionless surface inside which an object of mass $2 \mathrm{kg}$ is suspended. A constant force $F$ starts acting on the trolley as a result of which the string stood at an angle of $37°$ from the vertical (bob at rest relative to trolley). Then:

In the figure, the pulley $P$ moves to the right with a constant speed $u$. The downward speed of $A$ is $v_{\mathrm{A}}$ and the speed of $B$ to the right is $v_{\mathrm{B}}$.

In an imaginary atmosphere, the air exerts a small force $F$ on any particle in the direction of the particle’s motion. A particle of mass $m$ projected upward takes time $t_1$ in reaching the maximum height and $t_2$ in the return journey to the original point. Then

System shown in figure is in equilibrium and at rest. The spring and string are massless. Now the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x$ is