Two blocks $A$ and $B$ of mass $10 \mathrm{kg}$ and $40 \mathrm{kg}$ are connected by an ideal string as shown in the figure. Neglect the masses of the pulleys and effect of friction. $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

Two blocks of masses $10 \mathrm{kg}$ and $20 \mathrm{kg}$ are connected by a light spring as shown. A force of $200 \mathrm{N}$ acts on the $20 \mathrm{kg}$ mass as shown. At a certain instant the acceleration of $10 \mathrm{kg}$ mass is $12 {\mathrm{ms}}^{–2}$ towards right direction.

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: