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

A disc is kept on a smooth horizontal plane with its plane parallel to horizontal plane. A groove is made in the disc as shown in the figure. The coefficient of friction between mass $m$ and surface of the groove is $2/5$ and $\mathrm{sin\theta }=3/5$. Find the acceleration of mass with respect to the frame of reference of the disc.