In the arrangement shown in the figure, all pulleys are mass less and the strings are inextensible and light. Block $A$ has mass $M$. Select the correct statement $\left(s\right)$.

Three blocks $A,B$, and $C$ having masses $1\mathrm{kg}, 2\mathrm{kg},$ and $3\mathrm{kg}$, respectively, are arranged as shown in figure. The pulleys $P$ and $Q$ are light and frictionless. All the blocks are resting on a horizontal floor and the pulleys are held such that strings remain just taut. At moment $t=0,$ a force $F=40t \mathrm{N}$ starts acting on pulley $P$ along vertically upward direction as shown in the figure. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Regarding the times when the blocks lose contact with ground, which is correct? 

In the system shown in figure, $m_1>m_2$. The system is held at rest by thread $\mathrm{BC}$. Now thread $\mathrm{BC}$ is burnt. Answer the following;

Before burning the thread, what are the tensions in spring and thread $\mathrm{BC}$, respectively? 

Two blocks of masses $m_1$ and $m_2$ are connected with a light spring of force constant $k$ and the whole system is kept on a frictionless horizontal surface. The masses are applied forces $F_1$ and $F_2$ as shown in figure. At any time, the blocks have same acceleration $a_0$ but in opposite directions. Now answer the following.

The value of $a_0$ is 

A mass $M$ is suspended as shown in the figure. The system is in equilibrium. Assume pulleys to be massless. $K$ is the force constant of the spring. 

The extension produced in the spring is given by 

The elevator shown in figure is descending with an acceleration of $2 {\mathrm{ms}}^{-2}$. The mass of the block, $A=0.5 \mathrm{kg}$. Find the force (in Newton) exerted by block $A$ on block $B$.

Figure represents a painter in a crate which hangs alongside a building. When the painter of mass $100 \mathrm{kg}$ pulls the rope, the force exerted by him on the floor of the crate is $450 \mathrm{N}$. If the crate weighs $25 \mathrm{kg}$, find the acceleration (in $\mathrm{m} {\mathrm{s}}^{-2}$) of the painter.

A block is placed on an inclined plane moving towards right horizontally with an acceleration $a_0=g$. The length of the plane $\mathrm{AC}=1 \mathrm{m}$. Friction is absent everywhere. Find the time taken (in seconds) by the block to reach from $\mathrm{C}$ to $\mathrm{A}$.