Three blocks $A, B$, and $C$ of masses $10 \mathrm{kg}, 10 \mathrm{kg}$ and $20 \mathrm{kg}$ are arranged as shown in figure. All the surfaces are frictionless and string is inextensible. Pulleys and strings are light. A constant force $F=20 \mathrm{N}$ is applied on block $A$ as shown. Part of the string connecting both pulleys is vertical and part of the strings connecting pulleys with blocks $A$ and $B$ are horizontal. Then

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 $B$.