Blocks $A$ and $C$ start from rest and move to the right with acceleration $a_A=12t \mathrm{m} {\mathrm{s}}^{-2}$ and $a_C=3 \mathrm{m} {\mathrm{s}}^{-2}$. Here $t$ is in seconds. The time when block $B$ again comes to rest is

In the arrangement shown in figure $m_1=1 \mathrm{kg}, m_2=2 \mathrm{kg}$. Pulleys are massless and string are light. For what value of $M$ the mass $m_1$ moves with constant velocity (Neglect friction)

In the figure shown $m_1=1 \mathrm{kg}, m_2=2 \mathrm{kg},$ pulley is ideal. At $t=0,$ both masses touches the ground and string is taut. A force $F=2 t$ is applied to pulley ($t$ is in second) then $m_1$ is lifted off the ground at time $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass $m$ on a smooth horizontal surface is connected to a second mass $m$ by a light cord over a light frictionless pulley as shown. (Neglect the mass of the cord and of the pulley). A force of magnitude $F_{\circ }$ is applied to mass $m$ as shown. Neglect any friction. Find the value of force $F_{\circ }$ for which the system will be in equilibrium.

In the following diagram a massless pulley is pulled by a constant force of magnitude $p.$ There is no friction between the block and the floor. The acceleration produced in the block of mass $m$ is

The block $Q$ moves to the right with a constant velocity $v_0$ as shown in figure. The relative velocity of body $P$ with respect to $Q$ is (assume all pulleys and strings are ideal)

In the arrangement shown, the relation between acceleration of wedge $1$ and wedge $2$ is

In the situation given, all surfaces are frictionless, pulley is ideal and string is light, $F=\frac{mg}{2},$ find the acceleration of block 2 .